SOLUTION: Find the quadratic equation for the height of the arch of a bridge using the flowing facts: the horizontal length of the arch (from side to side) is 2000 feet, the lowest part

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Question 1161290: Find the quadratic equation for the height of the arch of a bridge
using the flowing facts: the horizontal length of the arch (from side
to side) is 2000 feet, the lowest part of the arch (on the far left
and far right) is 400 feet high, and the highest part of the arch (in
the center) is 1500 feet high. Let x be the horizontal distance from
the highest part of the arch and y be the height of the arch.
The equation is in the form
y=ax^2+b:
What is the value of a?
Give answer to four decimal places.
What is the value of b?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


In the equation y+=+ax%5E2%2Bb, the constant b is the height of the arch (y) when the distance from the highest point of the arch (x) is 0.

Since the highest point of the arch is 1500 feet, b is 1500.

So the equation is

y+=+ax%5E2%2B1500

To find the value of the coefficient a, use the height of the arch at either end.

The length of the bridge is 2000 feet, so the distance from the middle to one end is 1000 feet. The height of the arch at each end is 400 feet. So

400+=+a%281000%29%5E2%2B1500

Solve using basic algebra and round the answer to four decimal places, as directed.