Objective

• The objective is to provide an environment in which students can visualize when there are two solutions, only one unique solution, or no solution at all.

User´s Guide

• Drag each slider to change the numerical value of each corresponding coefficient.

1. The default settings produce a parabola that is away from the x-axis, that is, the graph does not cross the x-axis. This means that no x value can make the value of the function zero. Does this mean there is a solution or no solution at all?

2. Decrease the value of c until the parabola touches the x-axis at one point. How many unique solutions exist?

3. Keep decreasing the value of c. How many times does the parabola cross the x-axis? How many solutions should there be?