1. Let’s start with a problem today…Using only algebra, find
a cubic function with the given zeros. Answer should be in
standard form. Support by graphing your answer…labeling your
graph well!

2. Modeling with Higher-Order Polynomials
Sec. 2.3b…
Homework: p odd, 63, 67

3. Practice Problems
Dixie Packaging Company has contracted to make boxes with
a volume of approximately 484 cubic inches. Squares are to
be cut from the corners of a 20-in. by 25-in. piece of cardboard,
and the flaps folded up to make an open box. What size
squares should be cut from the cardboard?
Volume = (height)(length)(width)
Height = x
Length = 25 – 2x
Width = 20 – 2x 25 x x 20

4. Practice Problems
Dixie Packaging Company has contracted to make boxes with
a volume of approximately 484 cubic inches. Squares are to
be cut from the corners of a 20-in. by 25-in. piece of cardboard,
and the flaps folded up to make an open box. What size
squares should be cut from the cardboard?
Solve the equation:
Solve graphically!!! 25
Window: [0, 10] by [0, 1000] x
 Squares with length in.
or in. should be cut from
the cardboard x 20

5. Practice Problems 2 3, noncollinear
How many points do we need to determine a slant line?
How many points do we need to determine a quadratic function?
3, noncollinear
In general, we need (n + 1) points positioned with sufficient
generality to determine a polynomial function of degree n.
The process of fitting a polynomial of degree n to (n + 1)
points is called polynomial interpolation.

6. Practice Problems PERFECT!!!
Use cubic regression to fit a curve through the four points given
in the following table. x –2 1 3 8 y 2
0.5
–0.2
1.25
How good are the fits of these curves???
PERFECT!!!
Use quartic regression to fit a curve through the five points given
in the following table. x 3 4 5 6 8 y –2 –4 –1 8 3

7. Practice Problems U.S. Farm Exports Year Amount (billions) 1980 41.2
Try various polynomial regression
models (degrees n = 1, 2, 3, 4) for
the given data, and decide which
is the best model (let x = 0 be 1980).

8. Practice Problems Which is the best???
Try various polynomial regression models (degrees n = 1, 2, 3, 4)
for the given data, and decide which is the best model.
Linear model:
Which is the best???
(think graphically
and algebraically)
Quadratic model:
Cubic model:
Quartic model:

9. Practice Problems They need between 30 and 541 customers
Economists for Smith Brothers, Inc., find the company profit P
by using the formula P = R – C, where R is the total revenue
generated by the business and C is the total cost of operating
the business.
(a) Using data from past years, the economists determined the
revenue and cost functions below, where x is the number of
customers patronizing the business. How many customers must
Smith Bros. have to be profitable each year?
Where is this
function positive?
Graph
Window: [–10, 600] by [–1000, ]
They need between 30 and 541 customers

10. Where is the profit function
Practice Problems
Economists for Smith Brothers, Inc., find the company profit P
by using the formula P = R – C, where R is the total revenue
generated by the business and C is the total cost of operating
the business.
(b) How many customers must there be for Smith Bros. to realize
an annual profit of $60,000?
Where is the profit function
equal to the line?
Graph P(x) with the line y = 60,000
Either 201 or 429 gives a profit slightly over
$60,000; 200 or 430 customers both yield slightly
less than $60,000