Question

A rock is thrown from the side of a ledge. The height (in feet), x seconds after the toss is modeled by: h(x) = -4(x-4)2 +86 After how many seconds does the rock reach its highest point?

Answer 1

The height is modeled by a quadratic function.

`h(x)=-4(x-4)^2+86`

The equation is in the form:

`h(x)=a(x-b)^2+c`

In this form, the maximum occurs at x = b. And the maximum value is what we get when we plug in "b" into the function.

Matching the form and equation, we see that

b = 4

Hence, the maximum occurs at x = 4, or 4 seconds.

Thus,

The rocket reach its highest point after 4 seconds.