Solving Quadratic Equations

Square Roots

100

Solve the following quadratic equation by using square roots: x² = 4

x = 2 x = -2

200

Solve the following quadratic equation by using square roots: x² = 121

+11 or -11

300

Solve the following quadratic equation by using square roots: 4x² = 400

x = 10 x = -10

400

Solve the following quadratic equation by using square roots: x² -9 = -8

1 or -1

500

Solve the following quadratic equation by using square roots: 5x² + 3 = 128

x = 5 x = -5

Factoring

100

Factor the following quadratic equation: x² + 6x + 8 = 0

(x+2) (x+4)

200

Factor the following quadratic equation: 6x² + 37x + 6 = 0

(x+36) (x+1)

300

Factor the following quadratic equation: x² - 2x - 24 = 0

(x-6) (x+4)

400

Factor the following quadratic equation: x² + 10x + 16 = 0

(x+2) (x+8)

500

Factor the following quadratic equation: 2x² + 3x = 9

(2x-3) (x+3)

Zero Product Property

100

Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0

x = 7 x = -2

200

Use the Zero Product Property to solve the following quadratic equation. (x + 1)(x + 2) = 0

x = -2 x = -1

300

Use the Zero Product Property to solve the following quadratic equation. (2x - 7)(3x + 2) = 0

x = 7/2 or 3.5 x = -2/3 or -.67

400

Use the Zero Product Property to solve the following quadratic equation. (4x - 11)(3x + 4) = 0

x = 11/4 or 2.75 x = -4/3 or -1.33

500

Use the Zero Product Property to solve the following quadratic equation. (9x + 4)(10x - 1) = 0

x = -4/9 or -.44 x = 1/10 or .1

Quadratic Formula

100

What is the quadratic formula?

x = -(b) +- sqrt[(b)² - 4(a)(c)] /2(a)

200

Solve the following quadratic equation by using the quadratic formula: x² + 6x + 5 = 0

x = -1 x = -5

300

Solve the following quadratic equation by using the quadratic formula: x² - 9x + 20 = 0

x = 5 x = 4

400

Solve the following quadratic equation by using the quadratic formula: 2x² + 9x + 4 = 0

x = -1/2 x = -4

500

Solve the following quadratic equation by using the quadratic formula: 4x² - 17x - 15 = 0

x = 5 x = -3/4

Find The Vertex

100

A parabola formed by the equation of f(x)= -x² + 8x - 15 has x-intercepts at (3,0) and (5,0). What is the vertex of this parabola?

(4,1)

200

A parabola formed by the equation of f(x)= x²  - 2x has x-intercepts at (0,0) and (2,0). What is the vertex of this parabola?

(1,-1)

300

A parabola formed by the equation of f(x)= x² - 6x + 8 has x-intercepts at (2,0) and (4,0). What is the vertex of this parabola?

(3, -1)

400

A parabola formed by the equation of f(x)= -x² - 4x has x-intercepts at (-4,0) and (0,0). What is the vertex of this parabola?

(-2,4)

500

A parabola formed by the equation of f(x)= x2 - 9x + 14 has x-intercepts at (2,0) and (7,0). What is the vertex of this parabola?

(4.5, -6.25)