This parabola would have to be horizontal........since we can open it either to the left or the right, let's let it open to the right.....and since we can locate the vertex anywhere, let it be located at (-60, 60).......and we have
0 = a(0 - 60)^2 - 60
60 = a3600 divide both sides by 3600
1/60 = a
So.....the equation becomes
x = (1/60)(y - 60)^2 - 60
Here's the graph : https://www.desmos.com/calculator/fmvx6qjrro
Note : There are an infinite number of parabolas that would satisfy the original constraints