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