In this activity, students will discover the relationship between the degree and leading coefficient of a polynomial and the number of turns and end behavior of a graph. When complete, students will be able to describe the graph of any polynomial being given the equation only.
Before the Activity
Prior to this activity, students should have an understanding of polynomials, degrees, coefficients and standard form of a polynomial. It is suggested that students have previously graphed linear and quadratic functions.
During the Activity
The activity is designed to be completed by students individually with or without partner checks throughout.
After the Activity
Students can be given an assignment with more sample polynomial equations and asked to describe the graph. They can be given a chart similar to the one from the handout. A teacher may find adding the column indicating whether the end behavior is "same" or "different" may help students more. Further discussion needs to take place about the maximum number of turns and how that number can be reduced by an even whole number.