**MATH 107 QUIZ 4 ** Spring 2020

**NAME: **_______________________________

I have completed this assignment myself, working independently and not consulting anyone except the instructor.

**INSTRUCTIONS**

· The quiz is worth 100 points. There are 13 problems. This quiz is * open book* and

*. This means that you may refer to your textbook, notes, and online classroom materials, but*

**open notes***(and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than*

**you must work independently and may not consult anyone****Sunday, Feb 23**.

· __ Show work/explanation where indicated. Answers without any work may earn little, if any, credit. __You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also.

**In your document, be sure to include your name and the assertion of independence of work.**

· General quiz tips and instructions for submitting work are posted in the Quizzes module.

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

**1. (8 pts)** Look at the graph of the quadratic function and **state the intercept(s), vertex, and range, **and indicate which of equations A, B, C, or D, represents the graph. **[***No explanations required.*]

**Graph**

**Fill in the blanks **

**Equation**

State the* y*-intercept(s):

___________

State the range:

___________

State the vertex:

____________

The graph represents which of the following equations?

**Choice:** **_____**

A. *y* = *x*2 + 6*x* + 1

B. *y* = *x*2 – 6*x* + 1

C. *y* = –*x*2 + 6*x* + 1

D. *y* = –*x*2 – 6*x* + 1

**2. (4 pts) **Solve the inequality *x*2 ³ 7*x* and write the solution set in interval notation.

(no explanation required) Answer: __

A. [7, ¥)

B. (–¥, 0] È [7, ¥)

C. (–¥, 7] È [0, ¥)

D. [0, 7]

**3. (4 pts) ** For , use the Intermediate Value Theorem to determine which interval must contain a zero of f(x). (no explanation required) Answer: _____

A. Between 0 and 1

B. Between 1 and 2

C. Between 3 and 4

D. Between 2 and 3

**Solution:**

**4. (4 pts)** Translate this sentence about area into a mathematical equation.

The area * G* of a regular pentagon is directly proportional to the square of the length

*of its sides*

**S****Solution:**

**5. ** **(4 pts)** Solve and write **interval notation** for the solution set.

**Show careful algebraic work/explanation.**

**Solution:**

**6. (6 pts)** Each graph below represents a polynomial function. Complete the following table.

(no explanation required)

Graph

Graph A

Graph B

Is the degree of the polynomial **odd** or **even**? (choose one)

Is the leading coefficient of the polynomial **positive** or **negative**? (choose one)

**How many real number zeros** are there?

**7. (12 pts) **

Let When factored,

(a) State the domain.

(b) Which sketch illustrates the end behavior of the polynomial function?

A.

B.

C.

D.

Answer: ____

(c) State the *y*-intercept:

(d) State the *x*-intercepts:

(e) State which graph below is the graph of *P*(*x*). **__________**

GRAPH A. (below) GRAPH B. (below)

GRAPH C. (below) GRAPH D. (below)

**8. (8 pts) ** Let (no explanation required)

**Solution:**

(a) State the domain.

(b) State the *y*-intercept.

(c) State the *x*-intercept(s).

(d) State the vertical asymptote(s).

(e) State the horizontal asymptote.

**9.** **(8 pts)** Solve the equation__ Check__ all proposed solutions.

__Show work in solving and in checking, and state your final conclusion.__

**Solution:**

**10.** **(8 pts) ** Which of the following functions is represented by the graph shown below? **Explain **your answer choice. Be sure to take the asymptotes into account in your explanation.

A.

B.

C.

D.

**11. (8 pts)** For *z* = 5 + 2*i* and *w* = 8 – 3*i*, find *z*/*w*. Simplify as much as possible, writing the result in the form *a* + *bi*, where *a* and *b* are real numbers. **Show work**.

**12. (8 pts) ** Find the solutions of the equation . Find the complex solutions (real and non-real) of the equation, and simplify as much as possible. **Show algebraic work****.**

**Solution:**

**13.** **(18 pts) **

The marketing department has found that, when the new model calculators are sold at a price of *p* dollars per unit, the revenue R (in dollars) as a function of the price is:

(a) The revenue function is a quadratic function and so its graph is a parabola.

Does the parabola open up or down? _________

(b) What unit price should be established in order to maximize revenue?

(c) If this price is charged, what is the maximum revenue in $ ?