1. 5.8 Analyze Graphs of Polynomial Functions

2. Zeros, Factors, Solutions, and Intercepts.
Let
be a polynomial function.
The following statements are equivalent:
Zero:
K is a zero of the polynomial function f.
Factor:
(X – k) is a factor of the polynomial f(x).
Solution:
K is a solution of the polynomial equation f(x) = 0.
If k is a real number, then the following is also equivalent:
X-intercept:
K is an x-intercept of the graph of the polynomial function.

3. Graph the function: Solution: Since (x+2) and (x-1) are factors…
-2 and 1 are x-intercepts…
Plotting a few more points will determine the complete graph.

4. Graph the function: Solution: Local maximum Local mimimum
Since (x+2) and (x-1) are factors…
-2 and 1 are x-intercepts…
We will call these points turning points.
The turning points of the graph of a polynomial function are another important characteristic of the graph.

5. Turning Points of Polynomial Functions
The graph of every polynomial function of degree n has at most n – 1 turning points. Moreover, if a polynomial function has n distinct real zeros, then it’s graph has exactly n – 1 turning points.
You can use a graphing calculator to find the maximums and minimums of quadratic functions. If you take calculus, you will learn analytic techniques for finding maximums and minimums.

6. Use the graphing calculator to:
*Identify the x-intercepts
*Identify where the local maximum and minimum occur.