IM2 Solving Quadratic Equations

Factoring

100

x² - 1 = 0

{-1, 1}

200

Solve the following quadratic equation by factoring. 

x² - 6x + 5 = 0

{1, 5}

300

Solve the following quadratic equation by factoring.

 n² - 7n + 6=0

{6, 1}

400

Solve the following quadratic equation by factoring. 

b² - 8b = 20

{10, -2}

500

Solve the following quadratic equation by factoring. 

9x² + 5x - 24= 8x² + -5x

{-12, 2}

More Factoring

100

Solve the following quadratic equation by factoring:

 x² - 4 = 0

{-2, 2}

200

Solve the following quadratic equation by factoring:

9x² - 81x = 0

{0, 9}

300

Solve the following quadratic equation by factoring: 

(k - 3)(5k + 1) = 0

{3, -1/5}

400

Solve the following quadratic equation by factoring: 

5n² + 41n - 12 = -4 + 2n

{1/5, -8}

500

Solve the following quadratic equation by factoring: 

-2m² - 60m +72 = -8m² - 3m

{3/2, 8}

Completing the Square

100

Solve the following quadratic equation by completing the square: x² + 6x = -8

{-4, -2}

200

Solve the following quadratic equation by completing the square: x² - 6x = -5

 {1, 5}

300

Solve the following quadratic equation by completing the square: x² - 2x = 24

{-4, 6}

400

Solve the following quadratic equation by completing the square.  Round your answers to the nearest hundredth: x² + 10x +5 = 0

{-0.53, -9.47}

500

Solve the following quadratic equation by completing the square (nearest tenth): 

x² - 8x + 13 = 0

x = 5.7, x = 2.3

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.  Round your answer to the nearest hundredth: x² - 9x + 6 = 0

{0.72, 8.27}

400

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

{-1/2, -4}

500

Solve the following quadratic equation by using the quadratic formula (nearest tenth): 

4x² - 17x =-12 

{0.9, 3.4} 

Random Math Questions

100

What are three ways you can solve for the x-intercepts?

Completing the Square

Zero Product Property (factoring)

Quadratic Formula

Graphing 

200

What is the discriminant?

b²-4ac

300

Name three topics on this week's test.

Solving quadratics by completing the square, solving quadratics by graphing, factoring quadratics, solving quadratics using the quadratic formula

400

What is the standard form of a quadratic equation?

ax² + bx + c = 0

500

You and a friend are hiking in the mountains.  You want to climb to a ledge that is 20ft above you.  The height of the grappling hook you throw is given by the function h(t)=-16t² +32t +5.  What is the maximum height of the grappling hook?  Can you throw it high enough to reach the ledge?

The max height of the grappling hook is 21ft.  This is long enough to reach the 20ft ledge.