I am want to derive some of the equations for parabolas with vertex at (h,k). I wrote the equation below directly from the definition. I'm having a hard time obtaining any of the standard forms for parabolas from this definition. For example: y = a(x-h)^2 +K is one such equation I would like to derive. I need to know if I'm setting this up right.

As you can see I'm having trouble converting this into either form:

Where a =1/4p