6.2%20Evaluating%20and%20Graphing%20Polynomial%20Functions

1
6.2 Evaluating and Graphing Polynomial Functions
2
Objectives/Assignment

1. Evaluate a polynomial function
2. Graph a polynomial function
3. Assignment 15-79 odd

3
(No Transcript)
4
(No Transcript)
5
The degree of the polynomial.
A polynomial function is a function of the form
This is called the lead coefficient.
The constant term
All the exponents are whole numbers.
6
Here is a summary of common types of polynomial
functions.
Degree Type Standard Form
0 Constant
1 Linear
2 Quadratic
3 Cubic
4 Quartic
7
Recall to evaluate a polynomial you could use
direct substitution.
For example evaluate
when x 3.
Here is another way to evaluate a polynomial
function called synthetic substitution
2 0 -8 5 -7
3
x-value
105
ADD
6
18
30
10
35
98
6
2
Mult. By 3
f(3)98
8
Use synthetic substitution to evaluate the
polynomial at the given value. Check your result
by direct substitution.
9
Here are 4 graphs
Notice for each as
and
We call this the end behavior of a polynomial
function that is the value (y) of a function as
x approached positive infinity and negative
infinity.
10
Here are 4 more graphs
Notice again for each as
and
We call this the end behavior of a polynomial
function that is the value (y) of a function as
x approached positive infinity and negative
infinity.
11
For polynomial functions
The end behavior is determined by the lead
coefficient and degree.
n even
n even
n odd
n odd