HÀM SỐ BẮC HẢI

Đồ thị hàm số$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">c</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\ne </span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">0</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$y=ax^2+bx+c\trái(a\ne0\phải) $$y=một{x}^2+bx+c\left(một\ne 0\right)$$ là parabol có đỉnh là điểm

• $\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">TÔI</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\Delta </span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$I\left(-\frac{b}{2a};-\frac{\Delta}{4a}\right) $$TÔI\left(-\frac{}{2một};-\frac{}{4một}\right)$$

• $\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">TÔI</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\Delta </span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$I\left(-\frac{b}{a};-\frac{\Delta}{4a}\right) $$TÔI\left(-\frac{}{Một};-\frac{}{4một}\right)$$

• $\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">TÔI</span></span></span></span>}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span><span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\Delta </span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$Tôi\left(-\frac{b}{2a};\frac{\Delta}{4a}\right) $$TÔI\left(-\frac{}{2một};\frac{}{4một}\right)$$

Đồ thị hàm số$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">c</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">,</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\ne </span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">0</span></span></span></span>}$y=ax^2+bx+c,a\ne0 $$y=một{x}^2+bx+c,Một\ne 0$$ is parabol have a partition is a thẳng

• $\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}$x=-\frac{b}{2a} $$x=-\frac{}{2một}$$

• $\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}$y=-\frac{b}{2a} $$y=-\frac{}{2một}$$

• $\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span><span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}$x=-\frac{b}{a} $$x=-\frac{}{Một}$$

Cho number function$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">c</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\ne </span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">0</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$y=ax^2+bx+c\trái(a\ne0\phải) $$y=một{x}^2+bx+c\left(một\ne 0\right)$$ .

Từ đồ thị hàm số$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">f</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">⟹</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\mid </span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">f</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\mid </span></span></span></span>$y=f\left(x\right)\Longrightarrow y=\left|f\left(x\right)\right| $$y=f\left(x\right)⟹y=\left|f\left(x\right)\right|$$ bằng cách

• Giữ nguyên phần đồ thị$\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">f</span></span></span></span>}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$y=f\trái(x\phải) $$y=f\left(x\right)$$ on side$\mathrm{<span\; class="katex-container"\; data-idx="6"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Ô</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="6"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}$Con bò đực $$Ox$$ và lấy đối xứng phần đồ thị$\mathrm{<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">f</span></span></span></span>}<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$y=f(x) $$y=f(x)$$ ở phía dưới$\mathrm{<span\; class="katex-container"\; data-idx="4"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Ô</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="4"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}$Con bò đực $$Ox$$ qua$\mathrm{<span\; class="katex-container"\; data-idx="5"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Ô</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="5"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}$Con bò đực $$Ox$$ time drop the bottom$\mathrm{<span\; class="katex-container"\; data-idx="7"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Ô</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="7"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}$Con bò đực $$Ôx$$ .

• Giữ nguyên phần đồ thị$\mathrm{<span><span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span></span>}<span><span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span></span>\mathrm{<span><span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">f</span></span></span></span></span>}<span><span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span></span>\mathrm{<span><span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span></span>}<span><span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span></span>$y=f(x) $$y=f(x)$$ ở phía dưới$\mathrm{<span><span\; class="katex-container"\; data-idx="4"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Ô</span></span></span></span></span>}\mathrm{<span><span\; class="katex-container"\; data-idx="4"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span></span>}$Con bò đực $$Ox$$ và lấy đối xứng phần đồ thị$\mathrm{<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span></span>}<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span></span>\mathrm{<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">f</span></span></span></span></span>}<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span></span>\mathrm{<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span></span>}<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span></span>$y=f(x) $$y=f(x)$$ ở phía dưới$\mathrm{<span><span\; class="katex-container"\; data-idx="5"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Ô</span></span></span></span></span>}\mathrm{<span><span\; class="katex-container"\; data-idx="5"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span></span>}$Con bò đực $$Ox$$ qua$\mathrm{<span><span\; class="katex-container"\; data-idx="6"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Ô</span></span></span></span></span>}\mathrm{<span><span\; class="katex-container"\; data-idx="6"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span></span>}$Con bò đực $$Ôx$$

• lấy đối xứng phần đồ thị$\mathrm{<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span></span>}<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span></span>\mathrm{<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">f</span></span></span></span></span>}<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span></span>\mathrm{<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span></span>}<span><span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span></span>$y=f(x) $$y=f(x)$$ ở phía dưới$\mathrm{<span><span\; class="katex-container"\; data-idx="4"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Ô</span></span></span></span></span>}\mathrm{<span><span\; class="katex-container"\; data-idx="4"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span></span>}$Con bò đực $$Ox$$ qua$\mathrm{<span><span\; class="katex-container"\; data-idx="5"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Ô</span></span></span></span></span>}\mathrm{<span><span\; class="katex-container"\; data-idx="5"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span></span>}$Con bò đực $$Ôx$$

hai hàm số$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">c</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">></span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">0</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$y=ax^2+bx+c\trái(a>0\phải) $$y=một{x}^2+bx+c\left(một>0\right)$$ đồng biến trên$<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">đ</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">e</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$(đ; đ) $$(đ;e)$$ thì

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">đ</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">e</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\subset </span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$\left(d;e\right)\subset\left(-\frac{b}{2a};+\infty\right) $$\left(đ;đ\right)\subset \left(-\frac{}{2một};+\infty \right)$$

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">đ</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">e</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\subset </span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$\left(d;e\right)\subset\left(-\frac{b}{a};+\infty\right) $$\left(đ;đ\right)\subset \left(-\frac{}{Một};+\infty \right)$$

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">đ</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">e</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\subset </span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$\left(d;e\right)\subset\left(-\infty;-\frac{b}{2a}\right) $$\left(đ;đ\right)\subset \left(-\infty ;-\frac{}{2một}\right)$$

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">đ</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">e</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\subset </span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$\left(d;e\right)\subset\left(-\frac{b}{a};+\infty\right) $$\left(đ;đ\right)\subset \left(-\frac{}{Một};+\infty \right)$$

hai hàm số$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">c</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml"><</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">0</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$y=ax^2+bx+c\trái(a<0\phải) $$y=một{x}^2+bx+c\left(một<0\right)$$ ........ trên$<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">đ</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">e</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\subset </span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">b</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">Một</span></span></span></span>}}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">;</span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>$\left(d;e\right)\subset\left(-\frac{b}{2a};+\infty\right) $$\left(đ;đ\right)\subset \left(-\frac{}{2một};+\infty \right)$$

Cho Parabol $y=-x^2+2x-3$ có đỉnh là 

•  $I\left(1;5\right)$  

•  $I\left(1;2\right)$  

•  $I\left(1;-2\right)$  

•  $I\left(-1;-6\right)$  

hình parabol$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}$y=-x^2+2x-3 $$y=-x^2+2lần-3$$ have a participation is

$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}$x=-1 $$x=-1$$

$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}$x=1 $$x=1$$

$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}$x=2 $$x=2$$

Hình nào là đồ thị của$<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">P</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">:</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}$\left(P\right):y=x^2+2x-3 $$\left(P\right):y=x^2+2x\_-3$$

The best value${\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">tối\; đa</span></span></span></span>}}$y_{\max} $$y_{}$$ of number of function$\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">x</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}$y=-x^2+2x-3 $$y=-x^2+2lần-3$$ là

${\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">tối\; đa</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}$y_{\max}=1 $$y_{}=1$$

${\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">tối\; đa</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}$y_{\max}=-3 $$y_{}=-3$$

${\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">y</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">tối\; đa</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}$y_{\max}=-2 $$y_{}=-2$$

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