Department of Mathematics Education
J. Wilson, EMAT 6680

Quadratic Graph Demonstrations

by David Wise

The mathematics classroom continues to evolve into more and more of a student centered environment. Technology has played a major role in this movement by helping to make mathematics more visual, dynamic and real to students. Investigations that once were too difficult and/or time consuming to be feasible now are routinely accomplished with the help of technological tools. Mathematics students are spending more time being scientists (as they should), but this means teachers must sacrifice the amount of time they have the spotlight. As a result, teacher demonstrations have become increasingly more important in providing students with effective and efficient guidance and motivation to achieve curricular goals.

The following graphs are two examples of demonstration quality graphs, created so students can most easily see the similarities and differences between the equations within each example. By providing students with the "best" possible graph, students will be more likely to be able to make conjectures concerning the concept(s) the teacher is trying to introduce, or reinforce.

These demonstration graphs have been produced using the graphing calculator software, Graphing Calculator 2.2.1. If you do not have this software, you can use a demo version, or purchase the software through the internet at These demonstrations can also be created using other graphing software, or graphing calulators.

1. The role of c in the standard form of a quadratic equation.

y = x2 + x + c

y = x2 + x + 0

y = x2 + x + 2

y = x2 + x + 4

y = x2 + x - 2

y = x2 + x - 4








2. The role of a in the standard form of a quadratic equation.

y = ax2 + x + 2

y = -4x2 + x + 2

y = -3x2 + x + 2

y = -2x2 + x + 2

y = -x2 + x + 2

y = 0x2 + x + 2

y = x2 + x + 2

y = 2x2 + x + 2

y = 3x2 + x + 2

y = 4x2 + x + 2






Click here for another "view" of these equations.

These are just two of the endless examples of how to create more meaningful demonstrations for your students. A great natural extension of any demonstration is to challenge students to duplicate and/or extend demonstrations you have performed.

If you have any comments concerning this investigation that would be useful, especially for use at the high school level, please send e-mail to

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