Quadratics

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: (x+10)(x-10) = 300

x = 20 x = -20

400

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

1 or -1

500

Simplify the following quadratic expression: 98x² - 200

2(7x+10)(7x-10)

Solving Equations

100

4x²=256

x = 8

x = -8

200

Solve the following quadratic equation:  4x² = 24x 

x = 0 

x = 6

300

Solve the following quadratic equation: 

36 + (x - 3)² = 52

x =- 1

x = 7

400

Solve the following quadratic equation by completing the square: x² + 10x +16 = 0

x = -2 x = -8

500

Solve the following quadratic equation: 2x² - 8x = 10

x = 5

x = -1

Word Problems

100

A rock is thrown from the top of a tall building.  The distance, in feet, between the rock and the ground x seconds after it is thrown is given by f(x) = -16x²- 4x + 382 How long after the rock is thrown is it 340 feet from the ground?

1.5 seconds

200

 In an effort to catch a criminal; a superhero is going to leap over a building and take a short cut down the ally.  The function f(x) = -16x² + 150x gives the superhero's height in feet as a function of time.  The building is 425 feet high.  Will the superhero make it over the building?

No, his max height is about 352

300

A company models its net income, in thousands of dollars, with the function f(x) = 9x² – 54x – 144, where x is the number of units of its product sold.

How many units of its product does the company need to sell in order for the net income to equal $0?

8

400

 A fireworks rocket is launched from a hill above a lake.  The rocket will fall into the lake after exploding at its maximum height. The rocket's height above the surface of the lake is given by g(x)= -16x² + 64x + 80. How long will it take the rocket to hit the lake?

5 seconds

500

  A fireworks rocket is launched from a hill above a lake.  The rocket will fall into the lake after exploding at its maximum height.  The rocket's height above the surface of the lake is given by g(x)= -16x² + 64x + 80. What is the maximum height of the rocket?

144 

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=5x²-8x+3

(0.8,-0.2)