Print this document one-sided. If you are concerned about
the environment, you may

use recycled paper. Solve all problems in space provided. If you need more
space, you may

use the back of the page but be sure to indicate that in your solution. Each
problem is

worth an equal amount of points. For every problem be sure to show all the work.
Solutions

containing answers only will receive no or little credit. Make sure that your
solutions are

written legibly.

Team-work is not forbidden and, actually, encouraged,
however you are supposed to

submit solutions written by yourself.

You may use the textbook and notes as well as a scientific
calculator to solve the problems.

This is all you will ever need!

If you have problems with understanding the assignment,
please let your TA or me know

as soon as possible! Do not wait until the last minute!

1. Suppose that f(x) = 4x - 1 and g(x) = -2x + 5.

a) Solve f(x) = 0

b) Solve f(x) > 0

c) Solve f(x) = g(x)

d) Solve f(x)≤g(x)

e) Graph y = f(x) and y = g(x) and label the point that represents the solution
to

the equation f(x) = g(x)

2. Suppose that f(x) = 3x + 5 and g(x) = -2x + 15.

a) Solve f(x) = 0

b) Solve f(x) > 0

c) Solve f(x) = g(x)

d) Solve f(x)≤g(x)

e) Graph y = f(x) and y = g(x) and label the point that represents the solution
to

the equation f(x) = g(x)

3. The cost C, in dollars of renting a moving truck for a
day is given by the function

C(x) = 0.25x + 35, where x is the number of miles driven.

a) What is the cost if you drive x = 40 miles?

b) If the cost of renting the moving truck is $80, how many miles did you drive?

c) Suppose that you want the cost to be no more than $100. What is the maximum

number of miles that you can drive.

4. Using the graph transformations graph f(x) = x^2 - 6x - 1

5. Using the graph transformations graph f(x) = 2x^2 - 4x + 1

6. Draw the graph of f(x) = 2x^2 - x + 2, determine if
the graph opens up or down, find

the vertex, axis of symmetry, y-intercepts, x-intercepts, if any. Determine the
domain

and the range of the function. Determine where the function is
increasing/decreasing.

7. Draw the graph of f(x) = 4x^2 - 2x + 1, determine if
the graph opens up or down, nd

the vertex, axis of symmetry, y-intercepts, x-intercepts, if any. Determine the
domain

and the range of the function. Determine where the function is
increasing/decreasing.

8. Determine without graphing whether the given quadratic
function f(x) = -3x^2+12x+1

has a maximum value or a minimum value and then find the value.

9. Determine without graphing whether the given quadratic
function f(x) = x^2 + 6x + 9

has a maximum value or a minimum value and then find the value.

10. The graph of the function f(x) ax^2 + bx + c has vertex
at (0, 2) and passes through the

point (1, 8). Find a,b, and c.

11. Suppose that f(x) = x^2 + 4x - 21

a) What is the vertex of f?

b) What are the x-intercepts of the graph of f?

c) Solve f(x) = -21 for x. What points are on the graph of f?

d) Use the information obtained in the parts a) - c) to graph f(x) = x^2 + 4x
- 21.

12. The price p (in dollars) and the quantity x sold of a
certain product obey the demand

equation

a) Express the revenue R as a function of x. (Recall: R =
xp)

b) What is the revenue if 200 units are sold?

c) What quantity x maximizes revenue? What is the maximum revenue?

d) What price should the company charge to maximize revenue?

13. David has 400 yards of fencing and wishes to enclose a
rectangular area.

a) Express the area A of the rectangular as a function of the width w of the
rectangle.

b) For what value of w is the area largest?

c) What is the maximum area?

14. A farmer with 4000 meters of fencing wants to enclose
a rectangular plot that borders

on a river. If the farmer does not fence the side along the river, what is the
largest area

that can be enclosed?

15. A suspension bridge with weight uniformly distributed
along its length has twin towers

that extend 75 meters above the road surface and are 400 meters apart. The
cables are

parabolic in shape and are suspended from the tops of the towers. The cables
touch the

road surface at the center of the bridge. Find the height of the cables at a
point 100

meters from the center.