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