W. Gary Martin home page > CTSE 7970 > Write-up #1
CTSE 7970, Summer 2001, Write-up #1 – The behavior of parabolas
For this exercise, assume a thorough working knowledge of Algebra I, but no extensive prior experience with parabolas. That is, even if you “know” the answer, use Excel to explore the phenomenon, and explain without using any mathematics beyond Algebra I.
Give thorough, quantitative answers to each of the following questions, not just general impressions.
1. How do the constants in the general equation for a parabola effect its behavior?
a. Set up a spreadsheet to compute the values for any given parabola, y=ax2+bx+c.
- You will need to set up constants for a, b, and c… although c needs to be named something else.
- You will need to set up the domain for x, as in Lab 2 #2(c).
You should also add a graph showing your values.
b. What happens as you change the value of a? Explain, both in terms of the table of values and the graph.
- To make this easier to see, you may wish to disable the automatic scaling on the graph. To do that, double-click on the y-axis, and click on the “Scaling” tab. Then uncheck the “auto” box in front of each item. You will then need to enter reasonable values in those boxes.
c. What happens as you change the value of c? Explain, both in terms of the table of values and the graph.
d. Now take a look at what happens as you change the value of b.
- This may prove a little trickier. To help, you may want to display more than one parabola at a time. That is, keep the same values for a and c, but have a different value for b in different columns. See Lab 2 #3d for information on displaying multiple functions at once.
2. Now explore this equation for a parabola: y=a(x+b)2+c. How does each constant affect the parabola?
3. Finally, explore this equation for a parabola: y=a(x+b)(x+c). How does each constant affect the parabola?
4. Putting it all together.
a. What different insights do you gain by look at the table of values and the graph? What are the advantages and disadvantages?
b. Compare and contrast the three different forms for a parabola given in #1-3. What different information does each give about the behavior of a parabola? How could you use this to your advantage in understanding how a parabola works? Will each of these forms be equally useful for all parabolas?