**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.

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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

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The graphs illustrate this investigation.

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