Consider the diagram of the problem.
Let the vertex be on the y axis, exactly, at the point (0, 40)
Another point of this parabola is (200, 100), as can be checked from the figure.
The vertex form of the equation of a parabola is :
[tex]y=a(x-h)^{2}+k [/tex], where (h, k) is the vertex of the parabola,
replacing (h, k) with (0, 40), we have:
[tex]y=ax^{2}+40[/tex]
to find a, we substitute (x, y) with (200, 100):
[tex]100=a200^{2}+40[/tex]
40,000a=60
a=60/40,000=3/(2,000)
So, the equation of the parabola is [tex]y= \frac{3}{2000} x^{2}+40[/tex]
