Question

A bridge is supported by three arches. The function that describes the arches is

h(x) = -0.2x² + 3.0x, where h(x) is the height, in metres, of the arch above the ground at any distance, x, in metres,
from one end of the bridge. How tall is each arch?

Answer 1

11.25 meters

Explanation:

To find the maximum height of a parabola, we use the quadratic equation

x = -b/2a.

Given the equation (It's in Standard Form, Ax^2 + By = C)

So it's -3 / (2 * -0.2) which is equal to 7.5.

Now that we know the value of x, we plug in x into the equation.

-0.2(7.5^2) + 3.0(7.5) = height.

-0.2(56.25) + 22.5 = height.

-11.25 + 22.5 = height.

h(x) = 11.25