Quadratic Equations Review

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

Completing the Square

100

Graph the following equation: y=-3(x-2)² +4 

Vertex: (2,4) then down 3, 9, 15 (1a,3a,5a)

200

Graph the following equation: y=5(x+1)² -1

Vertex (-1,-1) then up 5, 15.... (1a,3a,5a)

300

Graph the following quadratic equation y = x² - 4x +1

vertex (2,-3) then up 1,3,5

400

Solve the following quadratic equation by completing the square: y = 2x² + 6x -1 

vertex (-1.5,-5.5) and up 2,6,10

500

Graph the following quadratic equation y =  2x² - 20x +51

Vertex (5,-1) then up 2,6,10 (1a,3a,5a)

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 - 9x + 20 = 0

x= 5   x=4

300

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

x = -1/2 x = -4

400

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

x = 5 x = -3/4

500

Solve the following quadratic equation by using the quadratic formula: 6x² - 17x + 12 = 0

x = 3/2  x = 4/3

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 y=5x²+4x+3

x =-2/5, 11/5