Precalculus: Products of Linear Functions

Objectives

• Students will understand relationships between the horizontal intercepts of two linear functions and the horizontal intercepts of the quadratic function resulting from their product.
• Students will understand relationships between the slopes of two linear functions and the orientation and width of the quadratic function resulting from their product.
• Students will understand when the product of two linear functions will not be quadratic.
• Students will explore the relationship between linear factors and the resulting cubic function.

Vocabulary

• linear function
• quadratic function
• cubic function
• roots
• intersect

About the Lesson

This lesson involves polynomial functions viewed as a product of linear functions.
As a result, students will:

• Manipulate linear functions to change the graph of their product to meet certain constraints.
• Make and test predictions about how the properties of linear functions affect the graphs of their quadratic or cubic product functions.