Hi Justin. This may not help, but who knows?

Define the bottom or top of the parabola at (d,D)

I'll rename your (x1,y1) to be (a,A), just because I feel like it.

And (x2,y2) is (b,B). And (x3,y3) is (c,C).

Also your "a" multiplier, I will call "N", as it makes the parabola **n**arrower.

Now if you get the point (d,D) and find N, then the equation for the parabola will be

(y-D) = N (x-d)^2

Okay, let's begin:

There are distance relationships in a parabola to do with squares,

hence we can write these equations:

N(a-d)^2 = |A-D|

N(b-d)^2 = |B-D|

N(c-d)^2 = |C-D|