Quadratic Equations Unit Review

Factoring/Square Root Method

100

Solve the following quadratic equation by factoring. x²+3x+2 = 0

x = -2 x = -1

200

Solve the following quadratic equation by using square roots: 4x² = 400

x = 10 x = -10

300

Solve the following quadratic equation by using square roots: 5x² + 3 = 128

x = 5 x = -5

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

Completing the Square/Quadratic Formula

100

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

x = -2 x = -4

200

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

x = 1 x = 5

300

What is the quadratic formula?

x = -b +- sqrt(b² - 4ac) /(2a)

400

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

x = -1/2 x = -4

500

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

x = 5 x = -3/4

Random

100

Find the discriminant then determine the number of solutions. 

y=-x²+7x-15

d = -11

0 solutions

200

Find the discriminant then determine the number of solutions. 

y=3x²-12x

d = 144

2 solutions

300

What is the vertex of the equation y=2x²+4x

(-1,-2)

400

Solve by method of choice

6x²=7x+5

{-1/2, 5/3}

500

The graph of a function is reflected over the x-axis, then two units left. What is the equations in vertex form?

y=-(x+2)²

Projectile Motion

100

Natalie threw a tennis ball over the fence and onto the court. The path of the ball can be described with the equation h=-16t²+18t+5.

What is the maximum height?

10.06 ft

200

Natalie threw a tennis ball over the fence and onto the court. The path of the ball can be described with the equation h=-16t²+18t+5.

How long until the ball hits the ground?

1.36 seconds

300

A circus acrobat is shot out of a cannon with an initial upward velocity of 50ft/s. The equation that models the acrobat's path is h=-16t²+50t+4

How long does it take the acrobat to reach their maximum height? 

1.5625 seconds

400

A circus acrobat is shot out of a cannon with an initial upward velocity of 50ft/s. The equation that models the acrobat's path is h=-16t²+50t+4

What is the acrobat's maximum height?

43.06 ft

500

A circus acrobat is shot out of a cannon with an initial upward velocity of 50ft/s. The equation that models the acrobat's path is h=-16t²+50t+4

How long until he hits the ground?

3.20 seconds

Graphing

100

Find the vertex of f(x)=-x²+8x-15

(4,1)

200

Find the vertex of f(x)=5x²+2x-2

(-1/5,-11/5)

300

Describe the transformation from the parent function

y=(x+4)²-1

Left 4, down 1

400

Describe the transformation from the parent function

y=2(x-5)²+4

Vertical stretch by 2, right 5, up 4

500

What is the domain and range of the quadratic y=x²-2x-5

Range - y is greater than or equal to -6

Domain - All Real Numbers