1. 5.2 Evaluate and Graph Polynomial Functions

4. 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.

5. Here is a summary of common types of polynomial functions.
Degree
Type
Standard Form
Constant 1
Linear 2
Quadratic 3
Cubic 4
Quartic

6. 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: 3
x-value
ADD
105 6 18 30 10 35 98 6
Mult. By 3 2
f(3)=98

7. Use synthetic substitution to evaluate the polynomial at the given value. Check your result by direct substitution.

8. 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.

9. 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.

10. n even n odd For polynomial functions:
The end behavior is determined by the lead coefficient and degree.
n even
n odd