Alg2H
More Higher Degree Functions as Math Models
1. The cubic function
WK#9b
that passes through the given points: (-1, 0), (2, 0), (3, 0), and (0, 9).
a) Write the particular equation of function
using two different methods. (One without
calculator!)
b) Check that all 4 points are on the graph of
.
c) State the local maximum of
d) State the local minimum of
2. You are designing a candle-making kit. Each kit will contain 25 cubic inches of candle wax and a
mold for making a model of the pyramid shaped building at the Louvre Museum in Paris, France.
You want the height of the candle to be 2 inches less than the length of each side of the candle’s
square base. What should the dimension of your candle mold be?
VRight Pryamid =
1
BH (where B is the area of base, H is height of Pyramid)
3
3. You are designing an open box to be made of a piece of cardboard that is 10 inches by 15 inches.
The box will be formed by making square cuts to each corner. You want the box to have the
greatest volume possible. How long should you make the cuts? What is the maximum volume?
What will the dimensions of the finished box be?
4. A Quonset hut is a dwelling shaped like a half cylinder. Supposed
you have 600 square feet of material with which to build a Quonset
hut.
where is the
a) The formula for surface area is
radius of the semicircle and is the length of the hut. Solve for
the length.
b) The formula for the volume of the hut is
. Write an
equation for the volume V of the Quonset hut as a polynomial function of r by substituting
the expression for l (part a) into the volume formula.
c) Use the function from part b to find the maximum volume of a Quonset hut with a surface
area of 600 square feet. What are the hut’s dimensions?