Experiment: Quadratic Systems

Objective

  • This experiment is designed to help visualize that solving a quadratic system is no different than solving a system of linear equations. The common point is to find the intersection of the solutions for each individual equation, thus helping students build the confidence necessary for solving systems of equations of higher degrees. This experiment provides an environment in which students can visualize when there are solutions and when no solution exists.

    The following specific system is used in the experiment:

                    x2/32 + y2/12 = 1
                    y = ax2 + bx + c

    in which each of the parameters "a", "b", and "c" can be changed to a desired value.

User´s Guide

  • Use sliders "a", "b", and "c" to change the value of the respective parameter.
Experiment: Quadratic Systems
Suggested Experiments

  1. Drag the slider bar "a" from left to right and from right to left to observe how this will change the shape of the equation y = ax2 + bx + c as well as the number of intersection points. What do these intersection points represent? Are these intersection points the solutions to the system? What does it mean when there is no intersection point?

  2. Repeat the experiment by changing the value of "b", or "c", or any combination of "a", "b", and "c".

 

Notice that the graph of the quadratic equation can extend outside the current drawing region.