An architectural engineer is designing a parabolic dome that will be 200 feet in diameter with a maximum height of 50 feet. find the equation of the cross–sectional parabola of the dome.

For the answer to the question above, 
diameter 200 means x-intercepts - 100 and 100 
maximum height = 50 means y-vertex = 50 

y = ax^2 +c 
c=50 

y =ax^2 + 50 
and 
ax^2 + 50 = 0 for x = + 100 and x = -100 

10000a + 50 = 0 

a = - 50/10000 
a = -5/1000 = - 0.005 

my answer is 

y = - 0.005 x^2 + 50