The function h(t) = −16t2 + 24t models the height, in feet, of a kangaroo t seconds after it jumps. What is the maximum height of the jump?

Accepted Solution

9 ftStep-by-step explanation:        The height of kangaroo after it jumps is represented by the function [tex]h(t)=24t-16t^{2}[/tex], where [tex]t[/tex] is in seconds, height is in feet.        To find the maximum height that the kangaroo jumps, we need to maximise [tex]h(t)[/tex].        The minimum/maximum value of a quadratic expression [tex]ax^{2}+bx+c[/tex] is given by [tex]\dfrac{4ac-b^{2}}{4a}[/tex].        As the coeffecient of quadratic term is negative, the function has a maxima.        Maximum value = [tex]\dfrac{4(-16)(0)-(24)^{2}}{4(-16)}=\dfrac{-576}{-64}=9[/tex].∴ Maximum height = 9 ft