Education Technology

# Activities

• ##### Subject Area

• Math: Algebra II: Polynomials

9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• ##### Software

TI-Nspire™ CX
TI-Nspire™ CX CAS

5.0

## Finite Differences

#### Activity Overview

Investigate the sets of finite differences for linear and quadratic functions.

#### Objectives

• Students will be able to recognize that the first set of finite differences for a linear function will be constant.
• Students will be able to recognize that the second set of finite differences for a quadratic function will be constant.
• Students will be able to determine the relationship between the constant set of first differences and the slope of a linear function.
• Students will be able to recognize that it is not possible to make inferences about the type of function from a set of data without further information.

#### Vocabulary

• finite differences
• constant
• degree
• linear, quadratic, and cubic functions
• rate of change
• slope

#### About the Lesson

This lesson involves an investigation into the sets of finite differences for linear and quadratic functions. As a result, students will:

• Calculate the first differences in a set of ordered pairs of a linear function.
• Relate the set of first differences in a linear function to the slope.
• Calculate the first and second differences in a set of ordered pairs of a quadratic function.
• Relate the sign of the second differences to the concavity of the quadratic function.
• Investigate a polynomial function where the second differences in a set of ordered pairs appear to be constant but are not.
• Investigate a function where none of the differences in a set of ordered pairs are constant.