SOLUTION: 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

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Question 620924: 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.
Answer by ankor@dixie-net.com(22740) (Show Source):
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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.
:
Using the form ax^2 + bx + c = y, in this equation c = 0
Two equation from the information given
:
Using the axis of symmetry and max: x=100; y=50
100^2a + 100b = 50
10000a + 100b = 50
:
Using the x intercept: x=200; y=0
200^2a + 200b = 0
40000a + 200b = 0
:
Multiply the 1st equation by 2, subtract from the above equation
40000a + 200b = 0
20000a + 200b = 100
---------------------subtraction eliminates b, find a
20000a = -100
a =
a = -.005
:
Find b using the 1st equation, replace a with -.005
10000(-.005) + 100b = 50
-50 + 100b = 50
100b = 50 + 50
100b = 100
b = 1
therefore the equation for this:
y = -.005x^2 + 1x
:
If we graph this, we can see what it will look like