So if you assume it starts at the origin, then two points you have are
You also have the maximum height of 35 feet. This occurs right in the centre of your x-intercepts.
So the turning point is .
If you use the turning point form for the equation of the parabola, it will be of the form
Substituting in the turning point gives
And substituting in another point, in this case gives you the a value.
Therefore the equation of the parabola is
Now use it to find the height when .