How do you get Standard Form, Vertex Form, and Intercept Form with the vertex of (2,7) and the points of (6,0) and (4,0)?

Question

I know the setup for the equations, but I cant figure out what goes where and what to do with the numbers...

Answer 1

vertex of (2,7) tells us that    y - 7 = a(x - 2)²   ⇐Vertex Form

 

the given fact that (4,0) satisfies this equation (is a point on the graph) leads us to calculate that 0 - 7 = a(4 - 2)²

and then a = -7/4...BUT

 

this contradicts the assertion that (6,0) is also a point on the curve.

 

This problem is over-specified.  Wrong, in short.