Math 011 Exam 4

1. State the quadratic formula .

2. State the formula for the x coordinate of the vertex.

3. A farmer wants to enclose three chicken coops with 150 feet of fencing. One side of the
coops will be the barn.

Find the equation for the area of the chicken coops.

4. ESL manufactures dictionaries. The cost of making x dictionaries per year is

C = .3x² - 12x + 80

and the revenue from selling x dictionaries per year is

R = -.7x² + 22x.

a. Find the equation for profit . (Profit = Revenue - Cost)

b. Graph the profit equation. Explain what the vertex, x intercepts, and y intercept
mean in terms of making dictionaries. Make sure you label the axis and use an
appropriate scale.

5. A cannon ball is shot straight up from the top of a canyon. The height of the cannon ball is
given by the equation

h = -16t² + 256t + 100

The graph of the height of the cannonball is given below.

You want to find out when the cannon ball will be 100 feet above the ground (h =
300). Graph this line on the graph above and find where the line intersects the
curve . (You should do this algebraically .)

6. Simplify

3(x ² - 4x + 2)- 2(x ² + 5x - 8)

7. Multiply

a. (x + 1)(x - 8)
b. (x - 6)²

8. Factor

a. 4x ² + 8x
b. x² + 2x -15
c. x² - 81