Solve the equation using the Square Roots Method: $$25x^2=4$$

$$x=-\frac{2}{5},\frac{2}{5}$$ .

Solve the equation using the Square Roots Method: $$9x^2-1=63$$

$$x=-\frac{8}{3},\frac{8}{3}$$ .

Solve the equation using the Square Roots Method: $$2x^2-3=49$$

$$x=-\frac{\text{sqrt}{26},\text{sqrt}{26}$$ .

What does it mean if a quadratic equation has no real solutions?

It means that the equation does not intersect the x-axis, and the solutions are complex or imaginary.

What is the general form of a quadratic equation?

The general form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

What is the significance of the discriminant in a quadratic equation?

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, no real roots.

How do you check your solution after solving a quadratic equation?

Substitute the solution back into the original equation to verify that both sides are equal.

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

The roots of a quadratic equation correspond to the x-intercepts of its graph, where the parabola intersects the x-axis.

What is a perfect square trinomial?

A perfect square trinomial is an expression of the form $$(a+b)^2 = a^2 + 2ab + b^2$$ or $$(a-b)^2 = a^2 - 2ab + b^2$$ .

What is the vertex form of a quadratic equation?

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

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula $$x = -\frac{b}{2a}$$ .

solving quadratics by square roots

Flashcard

•

Mathematics

•

9th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA-REI.B.4B, HSF-IF.C.7A, HSA.APR.C.4

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FLASHCARD QUESTION

Front

What is the Square Roots Method in solving quadratics?

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

What is the first step in using the Square Roots Method?

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

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