Polynomial & Rational Function Gallery
The following is a gallery of demos for illustrating selected families of polynomials and rational functions. These animations can be used by instructors in a classroom setting or by students to aid in acquiring a visualization background relating to the change of parameters in expressions for functions. Two file formats, gif and mov are available.
The gif animations should run on most systems and the file sizes are relatively small.
The mov animations require the QuickTime Player (version 6) which is a free download available by clicking here; these files are also small. (The mov files may not execute properly in older versions of QuickTime.)
The collection of animations in gif and mov format can be downloaded; see the zipped download category at the bottom of the following table.
We use abbreviations, GSP for Geometer's Sketch Pad 4 and EX for Excel spread sheet, VB for visual basic, and J for java to indicate the software used to generate the frames of the animation. If alternate corresponding software is also available there will be more than one abbreviation in that category. The VB software routines can be executed and the others can be downloaded.
Polynomials, Power Functions, & Rational Functions
Other Selected Resources:
A demo that includes quadratics
developed from the "locus of points"
definitions of the conic sections that can be implemented on a whiteboard (or
blackboard) is available at www.mathdemos.org.
Click on Go to
Demo List, then click on Physical
Demos, and finally click on 'Constructing
the Conic Sections on a Whiteboard'.
Another demo at www.mathdemos.org shows in an
immediate way that parabolas (quadratics) arise as graphs of natural phenomena. A ball is given a push up an inclined
plane. As the ball moves up and then back down the inclined plane its distance
from the starting point at the base is recorded by a motion sensor.
The time vs. distance data is simultaneously projected on a computer monitor.
When the ball returns to the starting point the data points are connected and
the resulting graph is parabolic. If we would continuously record the data the
resulting curve would indeed be a parabola. At
www.mathdemos.org. click on Go
to Demo List, then click on Physical
Demos, and finally click on 'Parabola!'.
There are a wide variety of
applets for graphing polynomials available; we mention just a few here.
graphing cubics ==> http://xanadu.math.utah.edu/java/CubicGraph.html
graphing quintics ==> http://www.math.umn.edu/~garrett/qy/Quintic.html
A
very nice applet for displaying cubics to
help users to relate the coefficients in a cubic polynomial to the shape of
its graph is available at http://thorin.adnc.com/~topquark/math/poly3nt.html
A picture of the applet shows basic directions and its
style.
The
US Air Force Acadamy has a nice collection of Mathematica notebooks on
mathematics topics including polynomials and rational functions; http://www.usafa.af.mil/dfms/mma/precalc.htm
NCTM
as part of their Illuminations collection has a interactive math applet combines the features of a
spreadsheet and a graphing calculator. It can be used as a
general tool or customized for specific purposes. For example,
this tool can be used to investigate polynomials, rational functions, and much
more. The applet can be downloaded from http://illuminations.nctm.org/mathlets/grapher/index.html
. Be sure to read their guidelines on the use and distribution of the
resource.
The
Function Institute at http://id.mind.net/~zona/mmts/functionInstitute/functionInstitute.html
has resources for polynomials, rational functions and more.
The
Math Forum at http://mathforum.org/mathtools/cell.html?rc=support&new_rc=tool
and the Math Archives at http://archives.math.utk.edu/
have a wide variety of resources for functions of they type displayed in
this gallery.
Credits:
The Geometer's Sketchpad routines were
constructed by Mark Yates of The McCallie School and are
used with his permission.
The Excel files were written by Xia Zhao, a student at Temple University, and David R. Hill, Temple University.
Special thanks to Deane Arganbright of University of Tennessee at Martin and to Walter Hunter of Montgomery County Community College for their assistance with the development of the Excel files that accompany this gallery. The book "Mathematical Modeling with Excel", by Erich Neuwrith and Deane Arganbright (BrooksCole) provides a rich source of information for developing Excel routines for mathematical instruction.
This gallery was developed by David R. Hill, Temple University.

8/10/03DRH Last updated 2/11/2005
As of 8/28/03