Juan hits a baseball. The equation $h=-16t^2+120t$models the height $h$, in feet , of the ball after $t$seconds. How long is the ball in the air?

An equation is a mathematical expression that contains an equal symbol $"="$.

A quadratic function, which is written in the form,$y=a{x}^2+bx+c$ where,$a\ne 0$ is called the standard form of the quadratic function.

The equation $h=-16t^2+120t$represents the height $h$, in feet $t$, of the ball after seconds. To calculate the time duration for which the ball is in the air,$h$should be equal to 0.

So, substitute$h=0$in $h=-16t^2+120t$.

localid="1647757137059" $$\begin{gathered} 0=-16t^2+120t \\ -8t\left(2t-15\right)=0 \\ t\left(2t-15\right)=\frac{0}{-8} \\ t\left(2t-15\right)=0 \end{gathered}$$

$t=0$or$2t-15=0$

$t=0$or$2t=15$

$t=0$or$t=\frac{15}{2}$

$t=0$or$t=7.5$

$t=0,7.5$

In this situation, these two points represent that the at the start $t=0$seconds the ball is at the ground level and after $t=5.625$seconds the ball will hit the ground level after traveling in the air.

Hence, for the duration of 5.625 seconds, the ball is in the air.