2.8 Analyzing Graphs of Polynomial Functions -Using the Graphing Calculator
1) Approximate Zeros of a Polynomial Function
2) Find Maximum and Minimum Points of a Polynomial Function
3) Find a Polynomial Model that fits a given set of data. (Cubic, Quartic Regression) and make predictions.

Identify the zeros (x-intercepts), maximums and minimums of
f ( x)  2 x 4  5 x 3  4 x 2  6

A rectangular piece of sheet metal is 10 in. long and 10 in. wide. Squares of side length x are cut from the
corners and the remaining piece is folded to make an open top box.
a) What size square can be cut from the corners to give a box with a volume of 25 cubic inches.
b) What size square should be cut to maximize the volume of the box? What is the largest possible volume of
the box?
Use your Graphing Calculator to find the appropriate polynomial model that fits the data. Use it to make predictions.
x
f(x)
1
26
2
-4
3
-2
4
2
5
2
6
16
…….. 10
?
The table shows the average price (in thousands of dollars) of a house in the Northeastern United States for 1987 to
1995. Find a polynomial model for the data. Then predict the average price of a house in the Northeast in 2000.
x
f(x)
1987
140
1988
149
1989
159.6
1990
159
1991
155.9
1992
169
1993
162.9
1994
169
1995
180
An open box is to be made from a rectangular piece of cardboard that is 12 by 6 feet by cutting out squares of side
length x ft from each corner and folding up the sides.
a) Express the volume of the box v( x) as a function of the size
x cut out at each corner.
b) Use your calculator to determine what size square can be cut from the corners to give a box with a volume of 40
cubic inches.
c) Use your calculator to approximate the value of
x which will maximize the volume of the box.