Factor the Quadratic Expression:

9x² - 36

9(x + 2)(x - 2)

Factor the following Quadratic Expression:

12x² + 36x + 27

3(2x+3)²

Factor the following Quadratic Expression:

2a² - 16a + 32

2(a - 4)²

Factor the following Quadratic Expression:

-6z² - 600

-6(z² + 100)

Factor the following Quadratic Expression:

10x² - 90

10(x - 3)(x + 3)

Solve the following Quadratic Equation:

x² + 2x = 6 - 6x

-8.69, 0.69

Solve the following Quadratic Equation:

6x² + 13x + 6 = 0

-3/2, -2/3

Solve the following Quadratic Equation:

2x² + x - 28 = 0

-4, 7/2

2x² + 8x = 5x + 20

-4, 5/2

Solve the following quadratic equation:

7x - 3x² = -10

-1, 10/3

Factor the quadratic expression:

.25t² - .16

(0.5t + 0.4)(0.5t - 0.4)

Factor the following quadratic expression:

8100x² - 10,000

100(9x - 10)(9x + 10)

Factor the folowing quadratic expression:

(x + 3)² + 3(x + 3) - 54

(x + 12)(x - 3)

6(x + 5)² - 5(x + 5) + 1

(2x + 9)(3x + 14)

Factor the following quadratic expression:

3(2a - 3)² + 17(2a - 3) + 10

2(a + 1)(6a - 7)

The area in square centimeters of a square area rug is 25x² - 10x + 1. What are the dimensions of the rug in terms of x?

(5x - 1) cm by (5x - 1) cm

The area in square feet of a rectangular field is x² - 120 x + 3500. The width, in feet, is x - 50. What is the length, in feet?

(x - 70) ft

The period of a pendulum is the time the pendulum takes to sqing back and forth. The function L = 0.81t² relates the length L in feet of a pendulum to the time t in seconds that it takes to sqing back and forth. A convention center has a pendulum that is 90 feet long. Find the period.

about 10.5 s

Suppose you have an outdoor pool measuring 25 ft by 10ft. You want to add a cement walkway around the pool. If the walkway will be 1 ft thick and you have 304 ft³ of cement, how wide should the walkway be?

about 3.6 ft

A town is planning a playground. It wants to fence in a rectangular space using an existing wall. What is the greatest area it can fence using 100 ft of donated fencing?

1250 ft²

The height of a projectile fired straight up in the air with an initial velocity of 64 ft/s is h = 64t - 16t², where h is height in feet and t is time in seconds. The table represents the data for another projectile.

a. Which projectile goes higher? How much higher?

b. At what times t will each projectile be at a height of 16 feet?

a. The projectile represented by the equation goes higher by 28 feet.

b. equation: t = 0.27 s and t = 3.73 s; table: t = 0.38 s and t = 2.62 s

Suppose you work for a packaging company and are designing a box that has a rectangular bottom with a perimeter of 36 cm. The box must be 4 cm high. What dimensions give the maximum volume?

• How can you model the volume of the box with a quadratic function?
• What informtion can you get from the function to find the maximum volume?

4 cm by 9 cm by 9 cm

The New River Gorge Bridge in West Virginia is the world's largest steel single arch bridge. You can model the arch with the function y = -0.000498x² + 0.847x, where x and y are in feet. How high above the river is the arch?

360 ft

The Zhaozhou Bridge in China is the oldest known arch bridge, dating to A.D. 605. You can model the support arch with the function f(x) = -0.001075x² + 0.131148x, where x and y are measured in feet. How high is the arch above its supports?

4 ft

A model for a company's revenue from selling a software package is R = -2.5p² + 500p, where p is the price in dollars of the software. What price will maximize revenue? What is the maximum revenue?

$100; $25,000