How to convert an arc to parabola?

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I've got a function that result's in an ascending arc form and with zero results in both ends. The only thing that matters is the maximum of the arc that always will be at the ending point of the arc. but we do not know the coordinates of the maximum point.

how can I convert this result to a parabola to help to find the maximum point? It's like having symmetry from the maximum point. like I said other results than maximum doesn't matter so zero parts can be non-zero or vice versa, but the maximum must be stable.

Example for the mentioned arc:

enter image description here

and the function is :

c1 = log2(1 + (sin(p) ^ 2) * 2 * 1000)
c2 = log2(1 + ((cos(p) ^ 2) * 2 * 10) / (1 + (sin(p) ^ 2) * 2 * 10))
if c1<1.5 or c2<1.5:
 c = 0 
else:
 c =(c1 + c2) ^ 3