Education Technology

# Activities

• ##### Subject Area

• Math: Precalculus: Polynomial, Power, and Rational Functions

9-12

20 Minutes

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

TI-Nspire™
TI-Nspire™ CAS

3.0

## Extreme Punkin' Chunkin'

#### Activity Overview

In this activity, students will explore extrema, zeros, and other key values of quadratic functions in real-world contexts.

#### Key Steps

• In Extreme Punkin' Chunkin’, students explore quadratic function graphs to identify extrema, zeros, and other key values of quadratic functions in real-world contexts. In the first two problems, students explore equations that model the launching of pumpkins from a medieval device called a trebuchet, which converts potential energy into kinetic energy.

• After graphing the model functions, students will use the Graph Trace tool to find the zeros, minimum or maximum and y-intercept. Throughout the activity, students provide responses to a variety of questions to assist them in developing understanding of the relevant patterns and skills.

• In addition to the Punkin Chunkin’ problems, students explore other problems involving profit maximization for an espresso stand and cost minimization for a company producing kayaks.

In each of these problems, students will use the same method as Problem 1, using the Graph Trace tool, to find the values of interest. Teacher discussion can include how to find these values algebraically.