GrafEq is an easy to use program for graphing equations encountered in the
secondary pre-calculus mathematics curriculum, which includes:
Equations may be entered in virtually any form.
To produce a certain ellipse, simply type in:
(x+1)^2/4^2 + (y-2)^2/3^2 = 1
GrafEq will typeset the equation as it is entered, which re-enforces standard math
conventions and provides clues to incorrect equation entry. Hints are also
shown which guide the user more directly, as when parentheses are not correctly balanced.
The program also features
successive refinement plotting,
which deletes regions of the plane that do not contain solutions,
revealing the regions that do contain solutions.
Plotting is completed by proving which pixels contain solutions.
This technique enables the graphing of implicit relations, in which no single variable
can be readily isolated. Such relations
cannot be graphed at all by the typical computer graphing utility
or graphics calculator.
Successive refinement plotting also permits the plotting of singularities.
GrafEq has been designed with the mathematics educator and secondary student in mind:
user-defined constants and
capability, file saving/loading and printout features
are useful in the classroom setting.
Typical uses of the program include topics such as:
The teacher can introduce enrichment topics, such as:
- rotation and shearing transformations,
- equations that determine regions (x = |x|).
The student can explore topics of interest.
(Visit our Tutorial pages.)
- “I wonder what the graph of the polar equation θ = cos r/tan r looks like?”
- “What happens to the graph if x is replaced with |x|?”
- “How do a catenary and a parabola differ?”
GrafEq takes full advantage of the capabilities of a laser printer: the teacher
can create printouts of exceptional quality for handouts or transparencies.
Files can also be printed with colour laser printers or colour inkjets.
Note: School site licenses include:
- in addition to the programs and user's manual (on 8.5" x 11" paper),
- a set of sample lessons, student handouts, and suggested enrichment topics—all on disk—for easy customizing and subsequent printing.