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# Sketching Graphs of Polynomial Functions

Lesson 5 of 9

## 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.

#### Warm-Up

*30 min*

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 3^{rd} 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.

#### Resources

*expand content*

- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: The Painted Cube Problem
- LESSON 2: The Painted Cube Part 2 and End Behavior
- LESSON 3: Surface Area and Volume Functions
- LESSON 4: Writing Rules for Polynomial Functions using Data Tables
- LESSON 5: Sketching Graphs of Polynomial Functions
- LESSON 6: Compare and Contrast Graphs of Polynomial Functions
- LESSON 7: Relationship between the Degree and the Number of X-intercepts of a Polynomial
- LESSON 8: Writing Equations for Polynomial Graphs
- LESSON 9: Graphing Polynomial Transformations