Question

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?

Answer 1

9 ft

Step-by-step explanation:

       The height of kangaroo after it jumps is represented by the function $h(t)=24t-16t^{2}$, where $t$ is in seconds, height is in feet.

       To find the maximum height that the kangaroo jumps, we need to maximise $h(t)$.

       The minimum/maximum value of a quadratic expression $ax^{2}+bx+c$ is given by $\dfrac{4ac-b^{2}}{4a}$.

       As the coeffecient of quadratic term is negative, the function has a maxima.

       Maximum value = $\dfrac{4(-16)(0)-(24)^{2}}{4(-16)}=\dfrac{-576}{-64}=9$.

∴ Maximum height = 9 ft