SOLUTION: A bridge over a railroad is supported by a parabolic arch. The clearance from the base to the top of the arch must be 40 metres. The inside distance between the supports is 120 met

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Question 1068649: A bridge over a railroad is supported by a parabolic arch. The clearance from the base to the top of the arch must be 40 metres. The inside distance between the supports is 120 metres. Write an equation that describes the arch. Show your graph.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So set up a coordinate system where (0,0) is on the road directly in the center.
The top of the arch would be (0,40) and the supports would be at (-60,0) and (60,0).
Using the vertex form,
y=a%28x-h%29%5E2%2Bk
y=a%28x-0%29%5E2%2B40
y=ax%5E2%2B40
So then using the support points,
0=a%28-60%29%5E2%2B40
3600a%2B40=0
3600a=-40
a=-1%2F90
So,
highlight%28y=40-x%5E2%2F90%29
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