Finding a parabolic equation with unknown variabilic constants?

[AtlasSniperma]

Hey folks,
Bit of a complex question here, but I'm hoping someone smarter than myself can help me figure this out. I want to make a parabolic curve that is controlled by 2 constants S and T. I know that in y = Ax² + Bx + C
C = S
as one of the points I can give from the if statements I'm working from gives the point (0,S)

the other 2 point however make it difficult for me to convert 3 points to the equation as, well, you'll see:

(T,100)
(T+100,100)

Can someone please help explain to me how to make these three points
(0,S) (T,100) (T+100,100)
into a parabolic equation without assuming a set value for either S or T

 

[Tinyboss]

Just a quick hint: the points (T,100) and (T+100,100) tell you that the parabola is symmetric about the line x=T+50, and so your equation has the form y=c+a(x-(T+50-b))(x+(T+50+b)) for some real numbers a, b and c.

Edit: Here's maybe a better hint: the x-coordinate of the vertex of a parabola is at -b/2a, so that tells you, in this case, that -b/2a=150, and since you've already got c nailed down, you're just one equation away from specifying a unique parabola.

 

[AtlasSniperma]

Thank you for your help. even with your "better hint"(a=1 b=-300) I can't figure out how to make it parabolic, no matter what I do its a linear line. I can give you 3 example C|T's so you can tell what I mean, but I can't figure out how to get it to go through the 3 points (point 4 it must satisfy is (2T+100, S))