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 :
![y=a(x-h)^{2}+k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E%7B2%7D%2Bk%20)
, where (h, k) is the vertex of the parabola,
replacing (h, k) with (0, 40), we have:
![y=ax^{2}+40](https://tex.z-dn.net/?f=y%3Dax%5E%7B2%7D%2B40)
to find a, we substitute (x, y) with (200, 100):
![100=a200^{2}+40](https://tex.z-dn.net/?f=100%3Da200%5E%7B2%7D%2B40)
40,000a=60
a=60/40,000=3/(2,000)
So, the equation of the parabola is