Math 107 quiz 4 | Algebra homework help

  

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 open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than 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 = x2 + 6x + 1

B. y =  x2 – 6x + 1

C. y = –x2 + 6x + 1

D. y = –x2 – 6x + 1

2. (4 pts) Solve the inequality x2 ³ 7x 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 S of its sides

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

4thdegIVT

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)

4thdeg.gif polycubic.gif 

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

4thdegdown.gif cubicpoly.gif

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.

q4ratl4.gif

A.

B.

C.

D.

 

11. (8 pts) For z = 5 + 2i and w = 8 – 3i, 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 $ ?

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