Park City Mathematics Institute Visualizing Functions Project Abstracts Drafts of Project Files (password required)

Where in the World are the Parabolas?

Mary Jo Hughes*, Sergio Zepeda, Rey Jope

The goal of this exercise is to assess student understanding of quadratic relationships. Students will complete a project using photographs of objects they see around them that appear parabolic. After placing the outline of the object on a coordinate grid, students model the curve with a table of collected values, determine an equation and justify whether a quadratic relationship is or is not the best model for the object's shape.

 

Maximizing iPhone Profits with Quadratics

Lori Bodner*, Faye Chiu, Scott Matthews

The goal of this activity is to introduce quadratic functions and to see how they differ from linear functions. Using real-life data collected from Apple iPhone sales, students will see how Apple's profits are closely tied to sales and prices of iPhones and that the function results in a parabola where there is a maximum point, or vertex. Working in small groups, students will analyze data between the retail price and profits of iPhones sales to determine the price of iPhones that will yield the maximum profit. They will create and examine the data graphically to identify the vertex of the function.

 

Projectile Motion and Parabolas

Connie Jaramillo*, Sandy Peterson

Using the software application LoggerPro3®, students will record the data given by the parabolic path of a basketball thrown into the air. The data will be written as ordered pairs using time as the independent variable and height of the ball as the dependent variable. Students will plot the data on graph paper and estimate the value of the vertex. The vertex, (h,k), will enable students to find the equation of the quadratic function in vertex form, y=a(x-h)2 +k. Algebra will help them find the value of "a". Students will enter the quadratic function into graphing calculators and work in pairs to investigate different transformations. They will explore the changes made to the vertex form of the quadratic equation to obtain each transformation. Students will then explain the connection between the transformations and the subsequent paths of the basketball.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.