precalculus quiz

QUIZ 2 Professor: Ms. Chowdhury MATH 115 Fall 2018 Name___________________________________ Date ________________ INSTRUCTIONS

The quiz is worth 55 points. There are 20 multiple choice (2 points) and 5 (3 points) short answer problems.

This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone.

You must show all of your work to receive full credit. If you do not show work, you may earn only partial or no credit at the discretion of the professor.

Please type your answers on the table in the separate answer sheet.Scanned handwritten work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module.

If you have any questions, please contact me by e-mail.

Please record your answer in the table below.

I have completed this assignment myself, working independently and not consulting anyone except the instructor and my notes. (If this part is not completed, you will receive a zero for the quiz)

Sign here __________________________________________ Date _______________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point.

1

1) f(x) = -4x2 + 12x

A) minimum; 3 2

, 9 B) maximum; 3 2

, 9

C) maximum; - 3 2

, - 9 D) minimum; - 3 2

, - 9

Divide and express the result in standard form.

2) 7 - 6i 6 + 5i

A) 72 11

- 71 11

i B) 72 61

+ 1 61

i C) 12 61

- 71 61

i D) 12 11

- 71 11

i

Find a rational zero of the polynomial function and use it to find all the zeros of the function.

3) f(x) = x3 + 2x2 - 9x - 18

A) {-3, 2, 3} B) {-2} C) {-3, -2, 3} D) {-3}

Find an equation for the line with the given properties.

4) The solid line L contains the point (2, 5) and is parallel to the dotted line whose equation is y = 2x. Give the equation for the line L in slope-intercept form.

A) y - 5 = 2(x - 2) B) y = 2x + b C) y = 2x + 3 D) y = 2x + 1

Find the average rate of change of the function from x1 to x2.

5) f(x) = 2x from x1 = 2 to x2 = 8

A) - 3 10

B) 1 3

C) 7 D) 2

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

6) f(x) = x2 + 6x - 9

A) (-3, -18) B) (6, 63) C) (3, 18) D) (-3, -36)

Find the product and write the result in standard form.

7) (7 + 7i)(7 - 9i)

A) 112 + 14i B) -63i2 - 14i + 49 C) -14 + 112i D) 112 - 14i

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8) (-7 + i)(-7 - i)

A) 49 B) -48 C) 50 D) -7

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero.

9) f(x) = 5(x2 + 1)(x + 4)2

A) -4, multiplicity 2, crosses the x-axis

B) -4, multiplicity 2, touches the x-axis and turns around

C) -1, multiplicity 1, crosses the x-axis; -4, multiplicity 2, crosses the x-axis

D) -1, multiplicity 1, crosses the x-axis; -4, multiplicity 2, touches the x-axis and turns around.

10) f(x) = 4(x - 4)(x + 3)3

A) 4, multiplicity 1, crosses x-axis; -3, multiplicity 3, touches x-axis and turns around

B) -4, multiplicity 1, crosses x-axis; 3, multiplicity 3, crosses x-axis

C) 4, multiplicity 1, crosses x-axis; -3, multiplicity 3, crosses x-axis

D) -4, multiplicity 1, touches x-axis; 3, multiplicity 3, touches x-axis and turns around

Find the zeros of the polynomial function.

11) f(x) = x3 + 4x2 + 4x

A) x = 0, x = -2 B) x = 0, x = 2 C) x = 0, x = 2, x = -2 D) x = 1, x = -2

Perform the indicated operations and write the result in standard form.

12) 3 -125 + 2 -20

A) -19i 5 B) 19 5 C) 19i 5 D) -19 5

Solve the equation by the method of your choice.

13) 9x2 - 53x - 6 = 0

A) - 1 9

, 9 B) - 1 9

, 6 C) - 1 9

, 1 53

D) {-9, 6}

14) 11x2 - 33 = 0

A) { 3} B) { - 3 , 3} C) - 33

11 ,

33 11

D) {- 33 , 33}

15) x2 + 16x + 47 = 0

A) {8 - 47, 8 + 47} B) {8 + 17}

C) {-16 + 47} D) {-8 - 17, -8 + 17}

3

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation.

16) 9x2 - 2x 0

A) (- , 0] 2 9

,

B) - 2 9

, 0

C) 0, 2 9

D) 0, 9 2

Solve the problem.

17) A herd of bison is introduced to a wildlife refuge. The number of bison, N(t), after t years is described by the polynomial function N(t) = -t3 + 25t + 120. Use the Leading Coefficient Test to determine the graph's end behavior. What does this mean about what will eventually happen to the bison population?

A) The bison population in the refuge will grow out of control.

B) The bison population in the refuge will die out.

C) The bison population in the refuge will reach a constant amount greater than 0.

D) The bison population in the refuge will be displaced by "oil" wells.

Solve the quadratic equation by the square root property.

18) 5(x - 9)2 = 10

A) {-9 ± 2} B) {-11, -7} C) {7, 11} D) {9 ± 2}

Solve the quadratic equation using the quadratic formula. Express the solution in standard form.

19) 16x2 - 5x + 1 = 0

A) - 5 32

± 39

32 B)

5 32

± 39

32 C)

5 32

± i 39

32 D) -

5 32

± i 39

32

4

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers.

20) f(x) = 9x3 - 6x2 + 2x - 7; between 1 and 2

A) f(1) = -2 and f(2) = -45; no B) f(1) = 2 and f(2) = 45; no

C) f(1) = 2 and f(2) = -45; yes D) f(1) = -2 and f(2) = 45; yes

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Complete the following: (a) Use the Leading Coefficient Test to determine the graph's end behavior. (b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. (c) Find the y-intercept. (d) Graph the function.

21) f(x) = -2(x - 2)(x + 3)3

Solve the problem.

22) An arrow is fired straight up from the ground with an initial velocity of 240 feet per second. Its height, s(t), in feet at any time t is given by the function s(t) = -16t2 + 240t. Find the interval of time for which the height of the arrow is greater than 224 feet.

23) You have 292 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.

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24) A box with an open top is formed by cutting squares out of the corners of a rectangular piece of cardboard and then folding up the sides. If x represents the length of the side of the square cut from each corner, and if the original piece of cardboard is 15 inches by 9 inches, what size square must be cut if the volume of the box is to be 110 cubic inches?

The graph of a quadratic function is given. Determine the function's equation.

25)

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