The goal for this activity is for students to use a graphing calculator to graph various polynomial functions and look for patterns as the degree of the polynomial changes. Students will describe the end behavior of many polynomial functions, and then will write a description for the end behavior of any polynomial function in general terms.
This investigation keeps students engaged and interested in the subject. It is a good learning opportunity to discover the effect of the degree of the polynomial on the graph. I suggest that it is done in pairs.
There are 4 polynomials on the second page where students are asked to:
a. Find all zeroes*
b. Describe the end behavior of each
c. Roughly sketch their graph, including the x-intercepts (without a calculator)
*Students already know how to find zeroes of polynomials. What's new is that now they will use end behavior to sketch graphs.
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