Parametric Equations Portfolio


I would like for you to create an original Parametric Equations problem
that will contain two parts: a "static" that will involve finding a solution
for one particular case, and a "dynamic" part of the problem will allow
you to investigate your problem under a "What-If-Not" lens. Your problem
should lend itself to being illustrated with an embedded GeoGebra applet.

Of your course, the page you create should be neat, organized, and above
all, mathematically correct and interesting.

Some parametric problems that you may want to refer to to get some
ideas are listed at right.

Your "static" problem should include the following:

  1. One or more lines or paths expressed in both standard and parametric form.
  2. A question about the speed of the object.
  3. A question of "when and where" something intersect something else.
  4. A question of "when and where" is something closest to something else.
  5. A question of "when and where" is something equidistant from two objects.

Your "dynamic" problem should take one of your questions and change one of the
question features in such a way that you will be able to investigate the problem
using GeoGebra.
Parametric problems to refer to
  • Page 4, #2 and #10
  • Page 5, #6 and #7
  • Page 6, #8
  • Page 7, #4 and #7
  • Page 8, #4 and #7
  • Page 10, #1 and #2
  • Page 11, #2 and #4
  • Page 12, #1 and #7
  • Page 13, #10 and #12
  • Page 14, #2 and #6 and #9 and #11
  • Page 15, #5
  • Page 16, #10
  • Page 17, #3 and #12 and #14
  • Page 20 #1 and #7 and #11

Your solutions should be solved algebraically using mathematical type (sitmo or wikitext), graphically using screenshots of your GeoGebra screen or embedded GeoGebra applets, and numerically using a GeoGebra spreadsheet. Examples of this type of GeoGebra problem solving can be found on the Rule of Four Template and the Rule of Four EXAMPLE

The following is a very lame example of bug problem


A bug is crawling along the line 3x+4y=12. When I first see the bug, it is at (4,0), and crawls 1 unit right and 3/4 units down every second.

What is a parametric equation that describes the position of the bug?

The bug starts at (4,0) and crawls 1 unit right and 3/4 units down. Therefore, a parametric equation of the bug could be




When does the bug cross the y-axis.

The bug crosses the y-axis when


Or in other words, 4 seconds before I started watching the bug

If you click on the TIME slider in the applet below, and if you use your arrow keys on your keyboard, you can change the value of time and see how the bug moves.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

The following is a very lame example of a WHAT-IF-NOT change of the problem:


The bug must be very careful when crawling along my graph paper. There is a frog at origin, whose tongue can dart out and snag any bug that is within 5 units of the frog. If the bug is crawling along the same path, how long is the bug in danger of snatched by the frog? How is the time spent in the danger zone related to the length of the frog's tongue?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

I notice from the applet that when the frog's tongue is 5 units long, the length of the danger zone is 8.77 units. Since the bug is crawling at a speed of 5/4 units per second, the bug spends a total of



So, when the frog's tongue is 5 units long, the time spent in the danger zone is 7.016 seconds.
When the frog's tongue is 4 units long, the time spent in the danger zone is...