Name:    Quiz 8-6: Solving Quadratic Equations

Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.

1.

Solve the equation. Check your solution. = 0
 a. 2, 5 c. 4, 7 b. 6, 9 d. 5, 8

2.

For the problem, define a variable. Then use an equation to solve the problem. The height of a triangle measures one foot more than twice its base. The area of the triangle is 18 square feet. Find the measures of the base and height of the triangle.
 a. h = 5 ft, b = 4 ft c. h = 8 ft, b = 4 ft b. h = 9 ft, b = 4 ft d. h = 11 ft, b = 5 ft

3.

For the problem, define a variable. Then use an equation to solve the problem. The length l of a rectangle is three times its width w. The area of the rectangle is 48 square centimeters. Find the measures of the sides.
 a. l = 12 cm, w = 4 cm c. l = 6 cm, w = 4 cm b. l = 5 cm, w = 15 cm d. l = 8 cm, w = 6 cm

4.

For the problem, define a variable. Then use an equation to solve the problem. Dominic’s kitchen is six feet longer than it is wide. The area of the kitchen is 72 square feet. Find the dimensions of the kitchen.
 a. 4 ft by 10 ft c. 6 ft by 12 ft b. 8 ft by 9 ft d. 7 ft by 13 ft

5.

For the problem, define a variable. Then use an equation to solve the problem. Find two consecutive even integers whose product is 48.
 a. 12, 14; –12, –14 c. 4, 6; –4, –6 b. 6, 8; –6, –8 d. 4, 12; –4, –12

6.

For the problem, define a variable. Then use an equation to solve the problem. Find two integers whose sum is 17 and whose product is 60.
 a. 6, 10 c. 5, 12 b. 8, 9 d. 7, 10

7.

Graph .
 a. c. b. d. 8.

Solve by graphing the related function. If the exact roots cannot be found, state the consecutive integers between which the roots are located. a. between 0 and 1 and between –4 and –3 b. between 1 and 2 and between –5 and –4 c. between 3 and 4 and between –7 and –6 d. between 2 and 3 and between –6 and –5

9.

What is the solution set of the equation 4(3m - 2)(m + 9) = 0?
 a. c. b. d. 10.

What is the solution set of the equation 75x2 - 50x = -8?
 a. c. b. d. 11.

What is the solution set of the equation n3 +2n2 - 35n = 0?
 a. {-7, 0, 5} c. {-5, 7} b. {-5, 0, 7} d. {-7, 5}

12.

The length of a rectangle is twice the width. The area is 72 square centimeters. What is the length?
 a. 48 cm c. 12 cm b. 24 cm d. 6 cm

13.

Which of the following equations describes the graph below? a. y - 2 = (x + 1)2 c. y = x2 + 4x + 9 b. y + 2 = (x + 1)2 d. y = x2 - 9x + 4

14.

If the roots of x + 4x + 1 = 0 are located by graphing the related function, between which pair of integers does a root of the equation lie?
 a. -4 and -3 c. 0 and 1 b. -2 and -1 d. 2 and 3

15.

How many real roots does x2 - x + 2 = 0 have?
 a. 0 c. 2 b. 1 d. cannot be detemined

16.

Solve x2 + 5x - 6 = 0
 a. 6, -1 c. -3, -2 b. -6, 1 d. 3, 2

17.

The perimeter of a rectangle is 49 cm. Its area is 117 cm2. If x represents the width of the rectangle in centimeters, which equation must be true?
 a. x(49 - x) = 117 c. x(x - 49) = 117 b. x( - x) = 117 d. x(x - ) = 117

18.

Solve the equation. Check your solution. 19.

For the problem, define a variable. Then use an equation to solve the problem. The length l of a rectangle is 4 meters more than its width w. The area of the rectangle is 45 square meters. Find the measures of the sides.

20.

For the problem, define a variable. Then use an equation to solve the problem. The height of a triangle measures 2 inches less than twice its base. The area of the triangle is 30 square inches. Find the measures of the base and height of the triangle.

21.

For the problem, define a variable. Then use an equation to solve the problem. The length of Jasmine’s house is 15 feet longer than it is wide. The area is 1000 square feet. Find the dimensions of the house.

22.

For the problem, define a variable. Then use an equation to solve the problem. Find two consecutive odd integers whose product is 143.

23.

For the problem, define a variable. Then use an equation to solve the problem. Find two integers whose difference is 12 and whose product is 45.

24.

Graph .

25.

Solve by graphing the related function. If the exact roots cannot be found, state the consecutive integers between which the roots are located. 