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

Answer:

Reasonable domain is [1.375,3].

Step-by-step 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 $t=-\frac{b}{2a}=-\frac{44}{2\left(-16\right)}=1.375$

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].