Roller Coaster Activity

The picture below is the monumental first hill of the Millenium Force, at Cedar Point. Like most roller coasters, the path of the track follows a parabolic curve. Your task is to find a way to match the red parabola to the curve of the track. Slide the a bar to change the coefficient of x-squared, and slide the c bar to change the constant. Stop when the red curve fits over the roller coaster.

Questions to consider:
What parabola fits the curve of the Force? How does changing the a slider affect the red parabola? How does changing the c slider affect the red parabola? Can you think of anything else that might be modeled with a parabola, like a roller coaster is?

Brian Bisignani, June 24, 2008, Created with GeoGebra