Sketching Graphs of Polynomial Functions

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Objective

Students will be able to sketch graphs of polynomial functions whose equations are written in factored form and to explain how the Zero Product Property is used to create these graphs.

Big Idea

Illuminate the key ideas of the Zero Product Property and continuity before learning and applying the algorithm for graphing polynomial functions whose equations are given in factored form.

Warm-Up

30 minutes

The warm-up includes two problems to review the main skills that students have learned so far: identify the type of function shown and writing a rule for a function given a data table, then matching equations to graphs and describing the end behavior of a function given the graph. The 3rd question is a preview for today’s lesson and students are not expected to fully solve this problem. I explain to students that I expect them to fully understand problem #1 and 2, and start to think about problem #3.

 

In thinking about problem #3, students can be presented with the formal definition of degree (write this on the reference poster with other key terms.) It is important that all students think about the “easy” points. Hopefully they will notice this without much coaching. Many of my students tried to guess the “End behavior.” I didn’t give them feedback on their guesses, because they will learn how to figure this out during the lesson.

Investigation and New Learning

30 minutes

Closing

10 minutes
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