Superlesson
Project 9-1
Algebra
Chapter 9
Quadratic Functions and Equations
What do the Leaning Tower of Pisa and mathematics have in common? Let's investigate!
Part A, Graphing Quadratic Functions
1. Galileo was a very interesting man. For a brief overview of his life, visit the Galileo Web site. Switch to Galileo's Experiments. Then run the experiment at that site by clicking on the inclined plane. Gather data for the total distance covered at one second intervals.
2. What is the relationship between the total distance covered and time?
3.Graph your data.
a.What shape is the graph?
b.Why does it not make sense to see data in Quadrant II?
c.Why does the site say distance is proportional to time squared?
Part B, Modeling with Quadratic Functions
4. Continue to use the Galileo site. Rewrite the distance equation in the form h = 1/2 at2 + vt + s.
5. In the above equation, why is a (acceleration) equal to -32?
6. Make a table for 1 second, 2 seconds, 3 seconds, and 4 seconds. Use the equation to calculate the height.
a. Graph you equation using a graphing calculator
b. Describe your graph.
Part C, Making Connections
7. Work with a partner. Make a model of Galileo's inclined plane experiment using a cardboard ramp as described in your text.
a. Gather the data for a 15-degree ramp and a 30-degree ramp.
b. Make a table of your data from 0, 1, 2, 3, and 4 even intervals on your ramp.
c. Write the equation that fits your data.
d. Graph this function.
8. Compare your work with other groups. What is similar? What is different?