Parabola from Roots

Slide the roots (A,B) left and right. You will notice the VERTEX V moves up and down as the roots get closer together or farther apart.

(1) Find a position for A,B that sets V exactly 1 unit above the X-axis.
(2) Find A,B to set V exactly 9 units above the X-axis.
(3) Make a RULE about the relationship between the height of V and the distance between A and B.
(4) Use algebra to PROVE your rule.

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Dave Mulkey, Created with GeoGebra