The purpose of this lesson is to expose students to a wide variety of graphs of polynomials and to identify important features. Students are introduced to the terms “degree,” “relative minimum,” and “relative maximum.” The degree of a polynomial is the highest exponent occurring on when the polynomial is written out as a sum of non-zero constants times powers of , with like terms collected. The relative minimum is a point on the graph of a function that is lower than any of the points around it, and the relative maximum is a point on the graph of a function that is higher than any of the points around it.

Students use precise language to describe expressions and make connections between polynomials and their graphs (MP6). Then by focusing on structure (MP7), students match equations and graphs of polynomials before creating equations and graphs of their own that meet specific criteria. This is meant to be informal and an opportunity for students to improve their skill graphing with technology while building their mental profile of what graphs of polynomials can look like.