Question

The function h(t) = −16t2 + 110t + 72 models the height h, in feet, of an object above ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?

Answer 1

We have the following function:

`h(t)=-16t^2+110t+72`

And this function models the height
`h`, in feet, of an object above ground
`t` seconds after being launched straight up in the air. The graph of this function is shown below. So we want to know what the number 72 represents. Well, what if
`t=0`?

If
`t=0` we have:

`h(0)=-16(0)^2+110(0)+72 \\ \\ \boxed{h(0)=72}`

Thus, 72 is the height of the object above the ground at
`t=0`. In other words, 72 is the initial height of the ball before being launched straight up in the air.