1. ( 20 points) (a) Use the
quadratic formula to determine the roots of the equation:2×2
+ x – 1 = 0. (see section 5.2)

(b) Determine the vertex of the parabola y = 2×2
+ x – 1. (recall, the x value of the vertex is given by x = -b/2a)

(c) Use parts a and b to sketch the graph of y =
2×2 + x – 1. You may wish to determine a few other “points that the parabola
passes through” to obtain a more accurate graph.

2. (15 points) How high will
a baseball that is thrown up into the air at 48 feet per second go if it starts its flight at a height
6 feet above the ground? (Hint, read section 3.5 carefully. This is anotherapplicationof
the quadratic, recall the x value of the vertex is given by x = -b/2a)

3. (25 points) (a) Section
4.2 Number 4. (b) Solve for x:
| x – 1 | = 4 (c) Sketch the graph of the
function y = | x – 1 | and use your graph to indicate your solution of part b.

4. (15 points) (a) Perform
the indicatedoperationand express the result in the form a + bi. (1 + ?5
)(1 – ?5 ) (b) Simplify. – i 11 (c)
Find all real numbers x and y that satisfy the
equation: -3x- 1 + 2yi = 4x – 5i. See example 11, section 5.3

5. (15 points) Section 2.7,
exercise number 8. Make sure that you compute the area.

6. (10 points) A rain gutter
is to be made up of rectangular aluminum sheets 12 inches wide by turning up the sides edges 90
degrees. What depth (of the edges) will provide a maximum cross sectional area
and thereby provide for the greatest flow of water? (Hint, think of quadratic
equations and that you want to maximize the “cross sectional area”.) Extra credit problems 1. The profit P, in
dollars, for a company that produces antivirus and systems utilities software
is: P = -0.0002×2 +140x – 250,000, where x is the number of units sold. What
sales level will yield a maximum profit?
2. A worker (on earth) dropped a screwdriver
from the top of anelevatorshaft. Exactly 5 seconds later he heard the sound
of the screwdriver hitting the bottom of the shaft. How tall is the elevator
shaft? 3. This is easier than you think. Try it. A bicycle
manufacturer has determined that when x hundred
bicycles are built, theaveragecostper bicycle is given by C(x) = 0.1×2 – 0.7 x +
2.425, where C(x) is in hundreds of dollars . How many bicycles should be built
in order to