Solving Quadratic Equations

Factoring

100

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

x = 7 x = -2

200

Solve the following quadratic equation by factoring. x²+3x+2 = 0

x = -2 x = -1

300

Solve the following quadratic equation by factoring. x² - 6x + 5 = 0

x = 5 x = 1

400

Solve the following quadratic equation by factoring. x² - 6x - 27 = 0

x = 9 x = -3

500

Solve the following quadratic equation by factoring. 2x² - 5x - 3 = 0

x = -1/2 x = 3

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

Find the Discriminant

100

Find the discriminant: x² + 6x = -8

Discriminant is 4

200

How many solutions will this equation have based on its discriminant: x² - 6x = -5

Discriminant is 16, so it will have two real solutions

300

How many solutions will this quadratic have based on its discriminant: x² - 2x + 24 = 0

The discriminant is -92 so no real solutions

400

What is the discriminant and what kind of solutions: x² + 9x +16 = 0

The discriminant is 17, so two rational solutions

500

Find the discriminant and tell me how many solutions: 3x² - 8x + 2 = 2x²-13

Discriminant is 4, so two real solutions

Quadratic Formula

100

What is the quadratic formula?

x = -b +- sqrt(b² - 4ac) /(2a)

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

Find the vertex of f(x)=-x²+8x-15

(4,1)

200

Find the vertex of f(x)=x²-2x

(1,-1)

300

Find the vertex of f(x)=5x²+2x-2

(-1/5,-11/5)

400

f(x)=-x²-4x

(-2,4)

500

Find the vertex of x=5y²+4y+3

(11/5,-2/5)