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.

 

 

To do your investigation using Graphing Calculator, click here.

 

 

 

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