Quadratics Review

Factoring

100

Solve the following equation by factoring: 

*HINT*: don't just factor it, actually solve it!

x^2 - 4x -32 

(x-8)(x+4) 

x =8, x= -4

200

Solve the following equation by factoring: 

*HINT*: pull out a GCF first!

3x^2 - 3x -90

3(x+5)(x-6)

x = -5, x = 6

300

Solve the following equation by factoring: 

*HINT* pull out a GCF if possible 

13x^2 -42x 

13x (x-3) = 0 

x = 0, x =3

400

Solve the following equation by factoring:

*HINT* If one term is missing, that term must =0.

9x^2 -1 = 0

(3x+1)(3x-1) = 0

x = -1/3 x = 1/3

500

Solve the following equation by factoring: 

*HINT* If a does not = 1 and there is no GCF, use the box!

15x^2 + 14x -8 

(5x-2)(3x+4)

x = 2/5 x = -4/3

Quadratic formula

100

What is the quadratic formula? 

-b +- sqrt(b^2 -4ac) / 2a

200

Solve the following equation by using the quadratic formula. You MUST use this method to get credit!

*HINT*: Make sure one side = 0 before beginning

x^2 = 2x +15

x = 5, x = -3

300

Solve the following equation by using the quadratic formula. You MUST use this method to get credit!

8x^2 = 15 - 14x 

x = 3/4     x = -5/2

400

Solve the following equation by using the quadratic formula. You MUST use this method in order to get credit! 

4x^2 - 6x = 14

x = 3+ sqrt(65) / 8     x = 3 - sqrt(65)/ 8

500

Solve the following equation by using the quadratic formula. You MUST use this method in order to get credit!

-2x^2 + 3x + 8 = 0

x = 3 - sqrt(73)/4    x = 3 + sqrt(73)/ 4

Completing the square

100

What value would be needed in order to make this equation a "perfect square?" 

x^2 -8x ___________ = 0 

16 

200

Solve the following equation. 

*HINT*: You should get two answers!

2(x-7)^2 - 8 = 0 

x = 9 and x = 5

300

Write the following equation in vertex form.

*HINT*: Check if it is already a perfect square!

x^2 -6x + 9 = 0

(x-3)^2 or (x-3)^2 + 0

400

Solve the following equation by completing the square. You MUST use this method in order to get credit!

x^2 + 12x + 4 = 0 

x = - 6 + sqrt(32)         x = -6 - sqrt(32)

500

Solve the following equation by completing the square. You MUST use this method in order to get credit! 

 

-2x^2 - 12x - 9 = 0 

x = -3 + sqrt(4.5)      x = -3 - sqrt(4.5)

Key Features

100

What are the x - intercepts of the following function? 

*NO CALCULATORS!!!*

(x - 5) ( x + 2) = 0 

(5, 0) and (-2, 0) 

200

What is the vertex of the following function?

*NO CALCULATORS!!!!*

-3 (x - 1)^2 + 6 = 0 

(1,6)

300

What is the y - intercept of the following function?

*NO CALCULATORS!!!!*

-3 (x - 1)^2 + 6 = 0 

(0, 3)

400

What are the x -intercepts of the following function? 

10x^2 = 6 + 9x

x = 1.34 x = -.446   or 

x =  9 + sqrt(321)/20      x = 9 - sqrt(321)/20

500

Identify the axis of symmetry, vertex and y - intercept of the following function: Must get all three correct and show work for credit.

-.5 (x - 1.5) ^2 - 1 = 0 

AOS : x = 1.5 

Vertex: (1.5 , -1) 

Y- intercept: (0, -2.125)

Word Problems

100

Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t^2 + 16t + 480, where h is height and t is time in seconds. How high was the cliff he jumped off of? 

*HINT* what is the y- intercept?   

480 feet 

200

2. If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation h(t) =-16t+128t. How long will it take the rocket to return to the ground??

t = 8 seconds 

300

A ball is thrown upwards from a rooftop, 80m above the ground. It will reach a maximum vertical height and then fall back to the ground. The height of the ball from the ground at time t is h, which is given by, h = -16t^2 + 64t + 80. How long will it take for the ball to hit the ground? 

Use any method you choose 

5 seconds 

400

Two consecutive even integers have a product of 360. Find the two numbers by using a quadratic function!

x (x + 2 ) = 360 

x = 18, x = 20

500

Let's revisit the situation from 300

A ball is thrown upwards from a rooftop, 80m above the ground. It will reach a maximum vertical height and then fall back to the ground. The height of the ball from the ground at time t is h, which is given by, h = -16t^2 + 64t + 80. 

This time, how long will it take the ball to reach it's maximum height? How high will it go? 

*HINT*: Get into vertex form! 

At 2 seconds, it will reach a maximum height of 144 feet