See attached

Do all steps with **brief explanations** similar to what was done in the examples in the notes.

**Before you do #3 read the note at the end of the exam.**

1. Find the area bounded by the following.

y = |x| and y = 4

2. Solve each system using either the elimination method or the substitution method. Verify your result by graphing each system. Indicate the point of intersection on your graph.

2x + y = 7

-2x + 3y = 5

Also, verify your result by graphing the system of equations given.

3. Two people set out simultaneously from two locations 12 miles apart and walk toward each other. One person walks 5 miles an hour faster than the other. Find the rate of speed of each person if they meet in one hour and ten minutes.

4. 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? See section 3.5.

5. (a) Solve -5 3x + 1 3 for x. Express your answer using a line graph and in interval notation.

Solve the following inequalities. Express your answer using interval notation.

(b) A car salesman has two choices for his salary.

Plan A A salary of $100 per week plus a commission of 3% of gross sales

Plan B A salary of $75 per week plus a commission of 5% of gross sales.

For what gross sales is plan B better?

(c) Solve |x + 3| = 2 for x.

(d) Sketch the graph of the function y = | x + 3 | and use it to verify your solution

of part c.

6. Sketch the graphs of the following equations by finding the intercepts and the vertex (recall the x coordinate of the vertex is x = -b/2a):

y = x2 + 3x + 1

(a) Use the quadratic formula to determine the roots of the equation

x2 + 3x + 1 = 0 to the nearest tenth.

(b) Determine the vertex of the parabola y = x2 + 3x + 1 to the nearest tenth. Hint, use the vertex formula given in section 3.2.

(c) Sketch the graph of y = x2 + 3x + 1 using the information you found in parts a and b. You might find it helpful to plot a few more points, for example, replace x by values like x = -1, x = 0, x = 1 etc . That is, find a few other x and y values to plot the curve.

7. (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 area.)

Extra.

1. This is easier than you think. Try it. The marketing department at Texas Instruments has found that when certain calculators are sold at a price of p dollars, the revenue (in dollars) as a function of the price is:

R(p) = -150p2 + 21,000p

(a) What unit price should be established in order to maximize revenue?

(b) If this price is charged what is the maximum revenue.

(c) Graph the function R(p).

2.Section 2.10 number 12.

Note:

Read sections 3.2, 3.3 and 3.5 carefully. These (and other) sections illustrate the power of the quadratic function in solving a variety of problems. To understand this function you must be able to graph it.

Some key thoughts :

(a) Any function of the form y = ax2 + bx + c where a

¹

0 is a quadratic.

(b) The formula x =

b

2a

–

gives you the x value of the vertex. Substitute this value in the equation (of part (a)) to find the y value.

(c) To sketch the graph of a quadratic one frequently need only know the vertex (x and y values) and the roots (found by solving ax2 +bx + c = 0 by factoring or by using the quadratic formula).

(d) the quadratic formula is:

2

-b±b-4ac

y =

2a

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