# Activities

• ##### Download

• • ##### Subject Area

• Math: Algebra I: Quadratic Functions
• Science: Physical Science: Energy

• ##### Author 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
Unit-to-Unit link cables

• ##### Other Materials
This is Activity 13 from the EXPLORATIONS Book:
EasyData Activities: Modeling Algebraic Functions with Data Collection Activities.

The following materials are required for this activity:
• Data from Activity 12: Bouncing Ball
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How High Will it Bounce?

#### Activity Overview

Students collect the height versus time data of a bouncing ball using the CBR 2™. They find the relationship between the bounce number and the bounce height. They also learn to graph scatter plots, calculate the maximum value of a parabola, analyze and find an exponential regression for the rebound height.

#### Before the Activity

• Use TI Connect™ to download Vernier EasyData™ application
• See the attached PDF file for detailed instructions for this activity
• Print pages 117 - 126 from the attached PDF file for the class

• #### During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

• Retrieve time and bounce height data from Activity 12: Bouncing Ball
• Record the X and Y coordinates of peaks as lists
• Mark the vertices and join the points
• Use the calculator to identify if a linear equation or an exponential equation is a better fit
• Notice both functions have coefficients close to one and their graphed functions are not distinctive when plotted
• Zoom and notice the exponential function is a better fit to the data peaks
• Find the equation for the exponential function in the form Y = ab^x
• Divide every vertex's Y-value by the previous vertex's Y-value, calculate the average and find the rebound percent
• Use it to calculate the height of each successive vertex of a bounce
• Use bounce height ratio, rebound percent, and initial drop height to write the exponential equation
• Compare this equation with the one generated by the calculator
• Determine how high the ball will bounce on its next bounce
• #### After the Activity

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