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Lesechka [4]
3 years ago
6

A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

nd (7, –13), and the center of the arch on the bridge is located at (0, 0). Find the equation of the arch of the bridge.
Mathematics
1 answer:
Zepler [3.9K]3 years ago
3 0
We can use the formula for a parabola: y = c(x - a) + b where
(a,b) is the origin of the parabola and c is some constant scaling factor.

We are given that the center of the arch on the bridge is (0, 0). This is our origin. So our equation is:

y = c(x - 0)^2 + 0 = cx^2

Now we just need to find c. We can do this by plugging in one of the other points given:

-13 = c*7^2
\frac{-13}{49} = c

So our final equation for the arch of the bridge is:

y = \frac{-13}{49}x^2
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