Untitled Document

Parabola Scavenger Hunt

Solve the following five problems. You will need to figure out where to get the tools to solve them from the list of web sites, below, or from other web sites. You may use Google or any other tool that you find useful. You may not play games, use AIM or chat. If you brought your book, you can use it.

Which is narrower, y = x² or y = 2x²?
What is the directrix of the parabola whose equation is y² = 20x?
Does a parabola appear to be wider or narrower if the focus is closer to the directrix?
Explain why a focus is called a focus. (Think satellite dish.)
For each of the following questions, provide crystal clear answers. If a equation of a parabola is of the form ax² + bx + c,

What does changing a do to the parabola?
What does changing b do to the parabola?
What does changing c do to the parabola?

Here are some spiffy web sites for exploring parabolas to help you solve these problems.

http://mathforum.org/mathtools/cell/pc,14.6.3,ALL,ALL/ (List of parabola sites)

http://www.math.com/tables/algebra/conics.htm (Nice start of cheat sheet at bottom of this page)
http://www.mste.uiuc.edu/dildine/sketches/parabola.htm (Explore how perpendicular bisectors of the line connecting the focus to points on the directrix run tangent to the parabola and thus form its shape.)
http://www.ies.co.jp/math/java/conics/draw_parabola/draw_parabola.html (Explore how the y values change on a parabola as the x values change. Explore how moving the directrix closer or further from the focus changes the shape of a parabola.)
http://www.ies.co.jp/math/java/conics/focus/focus.html (The applet shows why a satellite dish works. Imagine that the sky is off to the right…)

http://analyzemath.com/parabola/FindEqParabola.html (If you have an equation of the form y = a(x-h)² + k, you can see what it looks like with this applet. Might be a good way to check your work…)
http://www-groups.dcs.st-and.ac.uk/~history/Java/Parabola.html (Yet another form of equation of the parabola is y = ax2 + bx + c.
http://ca.geocities.com/xpf51/MATHREF/PARABOLA.html (This is a terrific tool for contrasting different ways to write equations of parabolas, see the numbers for intercepts, etc. Unfortunately, it wants x values that are in the first and second quadrants, so it has its limits. But it's still a great idea. Thanks to Natasha Walstra for finding this!)
Google is plain awesome. Note that the above web sites were among the top hits for the search "parabola applet". (An applet is a program, written in Java, that can have fun, interactive properties.)