# Classroom Activities

• ##### Subject Area

• Math: Algebra I: Quadratic Functions
• Science: Physics: Kinematics

9-12

60 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• TI-84 Plus C Silver Edition
• TI-84 Plus CE
• ##### Software

TI Connect™
TI Connect™ CE

• ##### Accessories

CBR™/CBR 2™
TI Connectivity Cable

• ##### Other Materials
This is Activity 12 from the EXPLORATIONS Book:
EasyData Activities: Modeling Algebraic Functions with Data Collection Activities.

The following materials are required for this activity:
• Bouncing ball
• ##### Report an Issue

Bouncing Ball

Published on 10/17/2008

#### Activity Overview

In this experiment, students collect the height versus time data of a bouncing ball using the CBR 2™. This activity investigates the values of height, time, and the coefficient A in the quadratic equation, Y = A(X - H)2 + K, which describes the behavior of a bouncing ball. They graph scatter plots, graph and interpret a quadratic function, apply the vertex form of a quadratic equation, and calculate the maximum value of a parabola.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print pages 105 - 116 from the attached PDF file for the class

• Set up the calculator and CBR 2™ for data collection
• #### During the Activity

Distribute the pages to the class.

• Drop a ball from a position 15 centimeters below a CBR 2 and collect data of it bouncing
• Plot the distance versus time data
• Analyze the data in one of three ways

• A. Analyze data from within App:
• Select region to be analyzed (parabola)
• Find the regression equation for the quadratic fit

• B. Exit the App and let calculator identify a regression equation:
• Plot the time versus distance data on the calculator
• Select a region and identify the data points from the region and store as lists
• Plot the data points (parabola) and find a regression equation for it

• C. Observing vertex form of parabola and it relationship with a quadratic equation:
• Use parabola plotted earlier with stored coordinates
• Store the coordinates from the vertex in the standard variables
• Enter equation A( X - H )2 + K, graph the equation, and explore different values of A
• Find value of A that best fits the parabola
• Since the ball is dropped, the value of A is negative and is found to be one-half the acceleration due to gravity
• #### After the Activity

• Students analyze the results and answer the case analysis questions on the student worksheet.
• Review student results
• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary