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1. An open box is to be made from a rectangular piece of material 15 centimeters by 9 centimeters be cutting equal squares from the corners and turning up the sides.

a. What is the maximum volume that the box can hold? ________________

b. What is the value of x if the volume of the box has to be 56cm3? ____________

2. An open box is constructed by cutting congruent squares from the corners of a 30 inch by 20 inch piece of aluminum. What are the dimensions of the largest box that can be constructed?

Length __________ Width ___________ Height ___________

3. An open box is to be made from a 10 inch by 12 inch piece of cardboard by cutting x inch squares from each corner and folding up the sides. Write a function giving the volume of the box in terms of x. What are the dimensions that maximize the volume of the box and what is the volume of the box?

V(x) = ______________________________

Length ________ Width ___________ Height ____________

4. The function P(x) = .018x3 - .687x2 + 6.638x + 16 describes the value of a precious metal over a 23-month period.

a. During which month did the metal achieve it’s greatest value?______________________

b. Determine the lowest value since then. ______________________

c. Describe the value of the metal over the last ten months. ______________________

d. If the P(x) continues to model the value of the precious metal, will the value exceed its previous greatest value in the next six months or will it drop below the previous low value (not the initial value)?______________________

5. The function M(x) = -0.287x3 + 8.8x2 – 59.843x + 220.7 describes the incidence of measles (per 100,000) for the period 1940-1960 (x = 0 for 1940).

a. In what year was the greatest incidence of measles reported? ______________________

b. According to the definition of M(x), what is the y-intercept? ______________________

c. Identify periods of increasing/decreasing frequency of the disease. __________________

d. If the function continues to model the disease beyond 1960, when did the incidence of measles approximate zero? ______________________

7. The average monthly basic rates R for cable television in the United States for the years 1988 through 1997 are given in the table, where t represents the time (in years), with t = 0 corresponding to 1990.

t |-2 |-1 |0 |1 |2 |3 |4 |5 |6 |7 | |R |13.86 |15.21 |16.78 |18.10 |19.08 |19.39 |21.62 |23.07 |24.41 |26.48 | |

a. Find a cubic model for the data using your calculator: _____________________________

b. Even though the model is relatively accurate for estimating the given data, do you think it is accurate to predict future cable rates? Explain ________________________________

6. Find all the real zeros f(x) = 2x3 – 3x2 – 3x – 5 _______________________________

7. Given the zeros of a function are -1 and 3 + 2i, find the original function.

______________________________

8. Find all the rational zeros of: [pic] _____________________________

9. The volume of a milk carton is 200 cubic inches. The base of the carton is square and the height is 3 inches more than the length of the base. What are the dimensions of the carton?

________________________________

10. Determine the left and right behavior of [pic].

_______________________________

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