# Unit_5_--_Lesson_3_--_Applications_of_Cubic_Functions_Updated_Fall2010

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Applications of Cubic Functions                                  Name ________________
Notes # _______                                                                 A common application of cubic
functions is
_________________

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.

Write the equation that models the volume of the box. _________________________________

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.

Write the equation that models the volume of the box. _________________________________

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. V(x) = __________________________

What are the dimensions that maximize the volume of the box and what is the volume of the box?
Length ________         Width ___________       Height ____________
Applications of Cubic Functions                                        Name ________________
Notes # _______
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? ______________________

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: f ( x)  x  x  34 x  56 _____________________________
3     2

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 f ( x)   x  x  3 x  2 .
3    2

_______________________________
Applications of Cubic Functions   Name ________________
Notes # _______

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