An architectural engineer is designing a parabolic dome that will be 200 feet

y = - 0.005 x^2 + 50  

Step-by-step explanation:

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