Question

A basketball is thrown upwards. The height f(t), in feet, of the basketball at time t, in seconds, is given by the following function: f(t) = −16t2 + 44t + 12 Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?

Answer 1

Reasonable domain is [1.375,3].

Explanation:

Given function is
`f\left(t\right)=-16t^2+44t+12`.

Now we need to find about what is the reasonable domain of the graph of the function
`f\left(t\right)=-16t^2+44t+12` when the basketball falls from its maximum height to the ground.

Compare with
`at^2+bt+c`, we get a=-16 and b=44

then t-coordinate of vertex
`t=-(b)/(2a)=-(44)/(2\left(-16\right))=1.375`

Then that means maximum height of the ball occurs when time t=1.375 seconds.

Now let's find time when ball falls on ground so set f(t)=0

`f\left(t\right)=-16t^2+44t+12`

`-16t^2+44t+12=0`

`4t^2-11t-3=0`

`\left(4t+1\right)\left(t-3\right)=0`

`4t+1=0` or
`t-3=0`

`4t=-1` or
`t=3`

`t=-0.25` or
`t=3`

Time can't be negative so we use t=3 only

Hence reasonable domain is [1.375,3].