Question

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) and (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.

Answer 1

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:

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