Solve by factoring: $$x^2 - 9x = 0$$

$$x(x - 9) = 0$$ ; Solutions: $$x = 0, x = 9$$ .

Solve: $$x^2 + 2x - 20 = 4$$

First, rearrange to $$x^2 + 2x - 24 = 0$$ ; Factoring gives: $$(x + 6)(x - 4) = 0$$ ; Solutions: $$x = -6, x = 4$$ .

Solve: $$3x^2 - 2x - 8 = 0$$

Factoring gives: $$(3x + 4)(x - 2) = 0$$ ; Solutions: $$x = 2, x = -\frac{4}{3}$$ .

What is the first step in solving $$x^2 + 6x - 13 = 3$$ ?

Make it equal 0 by subtracting 3 on each side: $$x^2 + 6x - 16 = 0$$ .

Solve: $$4m^2 - 100 = 0$$

Factoring gives: $$(2m - 10)(2m + 10) = 0$$ ; Solutions: $$m = -5, m = 5$$ .

What is the standard form of a quadratic equation?

The standard form is $$ax^2 + bx + c = 0$$ .

What are the roots of a quadratic equation?

The roots are the values of x that make the equation equal to zero.

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 real roots; if zero, one real root; if negative, no real roots.

A binomial is a polynomial with two terms, such as $$a + b$$ or $$x - 3$$ .

What does it mean for a quadratic to be factorable?

A quadratic is factorable if it can be expressed as a product of two binomials with rational coefficients.

What is the vertex form of a quadratic equation?

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

HW Lesson 7.2_Solving Quadratics by Factoring Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to factor a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, set the equation to zero, factor it into two binomials, and then set each binomial equal to zero to find the solutions.

4.

FLASHCARD QUESTION

Front

What is the zero product property?

Back

5.

FLASHCARD QUESTION

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Back

6.

FLASHCARD QUESTION

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Back

7.

FLASHCARD QUESTION

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