Solving Quadratic Equations

Factoring

100

x² - 1 = 0

{-1, 1}

200

Solve the following quadratic equation by factoring:

9x² - 81x = 0

{0, 9}

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}

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: x² + 10x +5 = 0

-5 +- 2(sqrt5)

500

Solve the following quadratic equation by completing the square: 

x² - 8x + 13 = 0

4 +-sqrt 3

Taking Square Roots

100

Solve the following quadratic equation  x²  = 16

{-4, 4}

200

Solve the following quadratic equation : x²  = -16

 {No solution}

300

Solve the following quadratic equation by completing the square: x² - 2 = 23

{-5, 5}

400

Solve the following quadratic equation. x² + 5 = 0

No Solutions

500

Solve the following quadratic equation: 

2x² -5 = 13

x = 3, x = -3

Quadratic Formula

100

What is the quadratic formula?

x =( -b pm sqrt(b^2 - 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 + 6 = 0

(9 pm sqrt(57))/2

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: 

4x² - 17x =-12 

x = (17 pm sqrt(97))/8

Projectile Motion

100

A ball is launched from a 269.28-foot tall platform. The function for the ball's height h at time t seconds after launch is h(t)=−16t²+131.2t+269.28, where h is in feet. When does the object strike the ground?

9.9 seconds

200

What year was the quadratic formula invented (the one we use today)

1594

300

A ball is launched from a 57.477-meter tall platform. The function for the ball's height h at time t seconds after launch is h(t)=−4.9t²+25.48t+57.477, where h is in meters. When does the object strike the ground?

6.9 seconds

400

What is the standard form of a quadratic equation?

ax² + bx + c = 0

500

A ball is launched from a 128-foot tall platform. The function for the ball's height h at time t seconds after launch is h(t)=−16t²+32t+128, where hh is in feet. When does the object strike the ground?

4 seconds