Question

Word problem involving the maximum or minimum of a quadratic function

Answer 1

Given the function of the height of the ball thrown vertically upward as;

$h(t)=44t-16t^2$

Where t is time taken it takes to get to the height.

The graph of the quadratic function is;

Thus, it has a maximum height.

At the maximum height;

$\frac{dh(t)}{dt}=0$

Thus,

$\begin{gathered} \frac{dh(t)}{dt}=\frac{d(44t-16t^2)}{dt}=0 \\ 44-32t=0 \\ 32t=44 \\ t=\frac{44}{32} \\ t=1.375\sec s \end{gathered}$

Now, we can get the maximum height at t = 1.375 seconds. We have;

$\begin{gathered} h(1.375)=44(1.375)-16(1.375)^2 \\ h(1.375)=60.5-30.25 \\ h(1.375)=30.25 \end{gathered}$

The maximum height the ball will reach is 30.25 feets.