1. Algebra 2
6.8 Analyzing Graphs of Polynomials
The following statements are ____________________________:
• k is a _________________ of the polynomial function f.
• x – k is a __________________ of the polynomial f(x).
• k is a _______________________ of the polynomial equation f(x) = 0.
• k is an __________________________ of the graph of the polynomial function f
if k is a real number.
1 2
EX1: Graph the function f (x) = ( ξ + 2 ) ( ξ − 1) .
4
1) What are the x-intercepts?
2) Are there any repeated roots? What does that mean for the graph?
3) What is the end behavior of the graph?
4) Make a table to find points between and beyond the x-intercepts.
x -3 -1 0 2 3
y
5) Graph the function.
What is the maximum for this function?
the minimum?
How many total max/min does this function have?
How many in comparison to its degree?

2. The graph of every polynomial function of degree n has at most ______________
“turning points.”
• A “turning point” is a local max or local min.
If a polynomial function has at n _________________, _______________ zeros, then its
graph has __________________ n – 1 turning points.
EX2: Maximizing
You are designing an open box to be made of a piece of cardboard that is 10 inches by 15
inches. You want the box to have the greatest volume possible. What is the maximum
volume? What will the dimensions of the finished box be?
HW p. 376 (14 – 18, 24 – 28, 36, 38 even)