Name:    Chapter 3 Post Test

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

1.

Select the graph of the quadratic function . Identify the vertex and axis of symmetry.
 a. Vertex: Axis of symmetry: -axis d. Vertex: Axis of symmetry: -axis b. Vertex: Axis of symmetry: -axis e. Vertex: Axis of symmetry: -axis c. Vertex: Axis of symmetry: -axis

2.

Determine the vertex of the graph of the quadratic function .
 a. b. c. d. e.

3.

Write the quadratic function in standard form.
 a. b. c. d. e.

4.

Find all the real zeros of the polynomial function and determine the multiplicity of each zero and the number of turning points of the graph of the function.

 a. All Real Zeros: 0,; Even multiplicity; number of turning points: 2 b. All Real Zeros: ; Even multiplicity; number of turning points: 1 c. All Real Zeros: 0,; Odd  multiplicity; number of turning points: 2 d. All Real Zeros: 0,1,; Even multiplicity; number of turning points: 3 e. All Real Zeros: ; Odd  multiplicity; number of turning points: 1

5.

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function.

 a. Zeros: d. Zeros: b. Zeros: e. Zeros: c. Zeros:

6.

Describe the right-hand and the left-hand behavior of the graph of .
 a. Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right. b. Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right. c. Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right. d. Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right. e. Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.

7.

Use the Remainder Theorem and synthetic division to find the function value.

 a. 6 b. 3 c. –3 d. 8 e. 7

8.

The amounts A (in billions of dollars) donated to support higher education in the United States from 2000 through 2007 are shown in the table, where t represents the year, with corresponding to 2000.

 Year, t Amount, A 0 23.3 1 24.3 2 24 3 24 4 24.5 5 25.7 6 28.1 7 29.9

Use a graphing utility to select a correct a scatter plot of the above data.
 a. b. c. d. e.

9.

Use synthetic division to divide.
 a. b. c. d. e.

10.

Use the Remainder Theorem and synthetic division to find the function value. Verify your

 a. –5 b. –6 c. –7 d. –10 e. 10

11.

Use synthetic division to divide.

 a. , b. , c. , d. , e. ,

12.

Use the Remainder Theorem and synthetic division to find each function value. Verify your

,
 a. –551 b. –545 c. –548 d. –549 e. –547

13.

Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals.

 a. b. c. d. e.

14.

Use the given zero to find all the zeros of the function.

 a. b. c. d. e.

15.

Find all the zeros of the function and write the polynomial as a product of linear factors.

 a. b. c. d. e.

16.

State sales tax is based on retail price. An item that sells for \$197.99 has a sales tax of \$11.4. Find a mathematical model that gives the amount of sales tax y in terms of the retail price x. Use the model to find the sales tax on a \$639.99 purchase. (Round your answer to four decimal places.)
 a. b. c. d. e.

17.

Use the fact that the diameter of the largest particle that can be moved by a stream varies approximately directly as the square of the velocity of the stream.

A stream with a velocity of   mile per hour can move coarse sand particles about 0.03 inch in diameter. Approximate the velocity required to carry particles 0.25 inch in diameter. (Round your answer to two decimal places.)

18.

Use the fact that the resistance of a wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area.

If #28 copper wire (which has a diameter of 0.0126 inch) has a resistance of 64.17 ohms per thousand feet, what length of #28 copper wire will produce a resistance of 33.5 ohms?

19.

The frequency of vibrations of a piano string varies directly as the square root of the tension on the string and inversely as the length of the string. The middle A string has a frequency of 400 vibrations per second. Find the frequency of a string that has 1.35 times as much tension and is 1.4 times as long.
 a. 361.97 vibrations / sec b. 331.97 vibrations / sec c. 341.97 vibrations / sec d. 371.97 vibrations / sec e. 351.97 vibrations / sec

20.

The electrical resistance, R, of a wire is directly proportional to its length, l, and inversely proportional to the square of its diameter, d.  A wire 80 meters long of diameter 4 millimeters has a resistance of 10 ohms. Find the resistance of a wire made of the same material that has a diameter of 3 millimeters and is 45 meters long.
 a. b. c. d. e.