Write up for Investigation 1

By

Jeffrey Frye

This exploration considers the graphs for different values of a, b, and c as the other two are held constant. In this investigation a and c are held constant at 1 and b is varied.

With these set of values, all parabolas will pass through the point (0,1). The change in b will move the parabola and change the vertex of the new parabola. As the b value is changed from -2<b<2, the original equation will have either 2 negative roots or 2 positive roots. At b=2, the parabola is tangent to the x-axis and has one negative root. At b=-2, the parabola is tangent to the x-axis and has one positive root. The locus of the vertices of all the parabolas is shown by the equation

The graphs illustrate this investigation.

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