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

Use TI Connect™ to download Vernier EasyData™ application
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.
Follow the Activity procedures:

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