How do you solve a quadratic equation by factoring?

To solve by factoring, rewrite the equation in the form $$(x - p)(x - q) = 0$$ , where p and q are the roots, then set each factor to zero: $$x - p = 0$$ and $$x - q = 0$$ .

What is completing the square?

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form $$(x - p)^2 = q$$ , making it easier to solve for x.

How do you graph a quadratic function?

To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts, then plot points and draw a smooth curve to form a parabola.

What is the significance of the coefficient 'a' in a quadratic function?

The coefficient 'a' determines the direction of the parabola: if a > 0, the parabola opens upwards; if a

What is the vertex form of a quadratic function?

The vertex form of a quadratic function is $$f(x) = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

How do you find the y-intercept of a quadratic function?

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, i.e., $$f(0) = c$$ in the standard form $$f(x) = ax^2 + bx + c$$ .

What is the relationship between the roots and the coefficients of a quadratic equation?

The sum of the roots (r1 + r2) is equal to $$-\frac{b}{a}$$ and the product of the roots (r1 * r2) is equal to $$\frac{c}{a}$$ .

Solving Quadratic Functions Flashcard

Student preview

14 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic function?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What is the vertex of a quadratic function?

Back

4.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

5.

FLASHCARD QUESTION

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

6.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

7.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

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