Question

A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow rainwater to drain. A cross-section of the road can be represented on a graph using the function f(x) = (x – 16)(x 16), where x represents the distance from the center of the road, in feet. Rounded to the nearest tenth, what is the maximum height of the road, in feet? 0. 1 0. 8 1. 3 1. 6.

Answer 1

The maximum height of the road which is made in such a way that the center of the road is higher off the ground than the sides of the road is 16 feet.

What is the maxima of parabola?

The maxima of a parabola is where, it opens down its vertex at the maximum point in a coordinate graph. By equating the derivative of equation of parabola equal to zero, it can be found out.

A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow rainwater to drain.

A cross-section of the road can be represented on a graph using the function,

$f(x) = (x - 16)(x+ 16),$

Here, x represents the distance from the center of the road, in feet.

This equation can be written as,

$f(x) = (x - 16)^2$

Now to find the maximum height, find the derivative of the above function as,

$f(x) = (x - 16)^2\\f'(x) = (x - 16)^2\\f'(x)=2(x-16)(1)\\f'(x)=2(x-16)$

Equate the above equation to zero as,

$0=2(x-16)\\0=x-16\\x=16$

Thus, the maximum height of the road which is made in such a way that the center of the road is higher off the ground than the sides of the road is 16 feet.

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