Solving Quadratics Review

Factoring Quadratics

100

Solve the following quadratic equation by factoring.

x² + 8x+ 15 = 0

x = -5 and x = -3

200

Solve the following quadratic by factoring.

x² - 121 = 0

x = -11 and x = 11

300

Solve the following quadratic by factoring.

3x² -2x - 21 = 0

x = -7/3 and x = 3

400

Solve the following quadratic by factoring.

4x² - 32x = 0

x = 0 and x = 8

500

Solve the following quadratic by factoring.

12x² - x - 35  = 0

x = 7/4 and x = -5/3

Square Root Method

100

Solve the following quadratic using the square root method.

3x² = 192

x = +-8

200

Solve the following quadratic using the square root method.

4x² + 1 = 577

x = +-12

300

Solve the following quadratic using the square root method. (Write your answer in simplest radical form)

-6x² - 13 = -445

x = +- 6√2

400

Solve the following quadratic using the square root method. (Write your answer in simplest radical form)

4(x - 3)² - 7 = 345

x = 3+- 2√22

500

Solve the following quadratic using the square root method. (Write your answer in simplest radical form)

2/3(x + 4)² - 9 = 79

x = -4 +- 2√33

Complete the Square

100

What is the formula we use to complete the square?

(b/2)²

200

Solve the following quadratic by completing the square.

x² + 4x - 6 = 0

x = -2 +- √10

300

Solve the following quadratic equation by completing the square.

x² - 8x - 4 = 0

x = 4 +- 2√5

400

Solve the following quadratic equation by completing the square.

x² -12x + 8 = 0

x = 6 +-2 √7

500

Solve the following quadratic equations by completing the square.

3x² - 18x - 12 = 0

x = 3 +- √13

Quadratic Formula

100

Find the value of the discriminant for the following quadratic.

4x² +2x +5

-76

200

How many real solutions does the following quadratic equation have based on the value of the discriminate?

4x² 12x + 9 = 0

One Real Solution

300

Use the Quadratic Formula to find the solutions to the following quadratic equation.

x² - 3x - 3 = 0

x = 3/2 +- √21/ 2

400

Use the Quadratic Formula to find the solutions to the following quadratic equation.

2x² + 18x + 39 = 0

x = -9/2 +- √3/2

500

Use the Quadratic Formula to find the solutions to the following quadratic equation.

5x² + 3x + 1 = 0

x = -3/10 +- i √11/10

Random

100

Find the product of the two binomials.

(2x - 3)(7x + 4)

14x² - 13x - 12

200

The graph/shape of a quadratic function is referred to as a ___________?

Parabola

300

The number i is defined to be equal to? 

√-1

400

A box falls from a warehouse shelf from a height of 16ft.  The function h = -16t² + 16 gives the height h (in feet) after t seconds.  

When does the box hit the floor?

When t = 1 or at 1 second

500

Using the velocity function: h = -16t² + v₀t + h₀

If a dirt bike is launched off a ramp with an initial height of 8 feet and an initial velocity of 20 ft/sec. 

When does the dirt bike land back on the ground?

Approximately 1.6 seconds