Set your parabola so that the vertex is at (0,90). This means the two intercepts with x-axis are (-60,0) and (60,0).

The equation of parabola can be written as:

y = ax^2 + bx + c, where a, b, and c are constants

Since the parabola goes trough (0, 90) we can write:

90 = a*x^2 + b*0 + c

c = 90

Now the equation is: y = ax^2 + bx + 90.

The parabola goes trough (-60, 0) and (60, 0) means:

a(-60)^2 - 60b + 90 = 0

a(60)^2 + 60b + 90 = 0

That is we have the following system of equations:

3600a - 60b + 90 = 0

3600a + 60b + 90 = 0

........

click here to see the system of equations solved for a and b

........

a = - 1/40

b = 0

The equation of the door is:

y = (-1/40)x^2 + 90