Exam 6				Sections 5.2, 6.1, 6.2, 6.7
100 Points																Name___________________________________
This test is due first thing Monday morning, 8:10 sharp.  It is hoped that this test will be a learning experience for you.  :o) 
SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question. 
Find an equation of the parabola described. 
1) 

Focus at ( 4, 0);   vertex at (0, 0) 

 

MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question. 
Match the equation to the graph. 
2) 

 =  8(y  + 1) 
A) 

 

B) 

 
C) 

 

D) 

 

 
SHORT ANSWER.  Write the word or phrase that best completes each statement or answers the question. 
Find the vertex, focus, and directrix of the parabola. 
3) 

 =  12y

 

Find an equation for the parabola described. 
4) 

Vertex at ( 5,  2);   focus at ( 3,  2) 

 

Find the vertex, focus, and directrix of the parabola with the given equation. 
5) 

 =  12(x  - 1) 

 

Find the vertex, focus, and directrix of the parabola. Graph the equation. 
6) 

 -  6x =  4y -  37

 
Solve the problem. 
7) 

A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is  16 inches across at its opening and is  3 feet deep, where will the light be concentrated? 
Hint:  Convert feet to inches.  We're asking you where the focus  is.

 

Verify that the values of the variables listed are solutions of the system of equations. 
8) 

x =  -2, y =  5 

 

Solve the system of equations by using substitution.  
9) 

 

Use the elimination method to solve the system. 
10) 

Hint:  Divide the first equation by 2 in your first step.

 

Identify variables in words and units.  Write the system of equations. 
11) 

The Family Fine Arts Center charges $ 24 per adult and $ 10 per senior citizen for its performances. On a recent weekend evening when  455 people paid admission, the total receipts were $ 6496. How many who paid were senior citizens? 

 
The following system has no solution.  Explain how you can tell.  What's the geometry of this situation? 
12) 

 

Solve the system of equations. 
13) 

 

Identify variables and write the system of equations for the following problem. 
14) 

Lexie wants to have an income of $9000 per year from investments. To that end she is going to invest $90,000 in three different accounts. These accounts pay 7%, 10%, and 14% simple interest. If she wants to have $10,000 more in the account paying 7% simple interest than she has in the account paying 14% simple interest, how much should go into each account? 

 

Explain how you can tell that #15 has no solution. 
15) 

 

This system has infinitely many solutions.  Solve it and state the general solution, for instance, 
x = 3z - 2, y = 2z + 7, z = any real number. 
16) 

 

Write the augmented matrix for the system.  Do not solve. 
17) 

 

 

Write the system of equations associated with the augmented matrix. Do not solve. 
18) 

 

Perform the row operation(s) on the given augmented matrix. 
19) 

=  

 

20) 

  = 4 + 

 

Graph the inequality. 
21) 

3x  + 5y ≤  15

 
22) 

y >   + 3

 
Graph the system of inequalities. 
23) 

 

 
1) 

y2 =  16x 

2) 

A 

3) 

vertex: (0, 0)
focus: (0,  3)
directrix: y =  -3

 
4) 

 =  -8(x -  5) 

5) 

vertex:  ( 1,  3)   
focus:  ( 4,  3)   
directrix:  x =  -2 

6) 

vertex: ( 3,  7)
focus: ( 3,  8)
directrix: y =  6

 
7) 

0.4 in. from the vertex 

8) 

solution 

9) 

x = 5, y = -2 

10) 

x =  8, y =  -8 

11) 

316 senior citizens 

12) 

inconsistent (no solution) 

13) 

x =  1, y =  -5, z =  4 

14) 

$40,000 at 7%, $20,000 at 10%, $30,000 at 14% 

15) 

inconsistent (no solution) 

16) 

x = -3z - 5
y = z + 2
z = any real number 

17) 

 
18) 

 
19) 

 
20) 

 
21) 

 

22) 

 

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