In this lesson, students apply the connections they have been making between graphs and equations of polynomials. Students begin by comparing the possible graphing windows of two polynomial functions, where one is a multiple of the other. 

Next students critique the reasoning of others (MP3) as they consider a statement about a polynomial function, given an equation and a graph. Again, students must identify an appropriate graphing window for the function.

Then students write possible equations for a polynomial, given specific horizontal intercepts, connecting the ideas of horizontal intercepts, factors, and zeros. The important takeaway of this lesson is that a polynomial with a factor of has a zero when . Students will continue to use this idea throughout future lessons as they build up to the Remainder Theorem, which allows us to prove that a polynomial with a zero at must have as a linear factor.