In the following example drag the points labeled "a", "h", and "k" to change the respective values in the equation y=a(x-h)²+k and see the effect of these changes in the graph. 

Note: In the applet below the equation y=a(x-h)²+k is displayed as y=a(x-h)^2+k with the actual values for a, h, and k.

Do the following:

1. Modify h and k to find a parabola whose vertex is at the point (2,1). Does changing the value of a change the vertex?

2. Modify a, h, and k to find an equation of a parabola that passes through the 2 green points.

3. Is this the only parabola that passes through the 2 green points?

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