# A bridge is built in the shape of a parabolic arch. The bridge has a span of 50 meters and a maximum height of 40 meters. How do you find the height of the arch 10 meters from the center?

##### 1 Answer

May 16, 2016

#### Explanation:

Referring to the highest point as the origin O and the the altitude

from O as the x-axis, the equation of the parabola is

From the data given, the ends of the bridge are at

So,

When, at 10 meters from the center,

there is

From the equation of the parabola,

6.4. And so, the required height

The graph for the arch is in a befitting frame.

graph{(y-40+0.064x^2)(y)=0[-25 25 -40 40]}