The height is modeled by a quadratic function.
[tex]h(x)=-4(x-4)^2+86[/tex]The equation is in the form:
[tex]h(x)=a(x-b)^2+c[/tex]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.
