Question

an object was launched off the top of a building. the function ( f(x)=-16 x^{2}+48 x + 64 ) represents the height of the object above the ground, in feet, ( x ) seconds after being launched. find and interpret the given function values and determine an appropriate domain for the function.
( f(-1)=square ), meaning that ( square ) seconds after the object was launched, the object was ( square ) feet above the ground. this interpretation ( square ) in the context of the problem.
( f(0.5)=square ), meaning that ( square ) seconds after the object was launched, the object was ( square ) feet above the ground. this interpretation ( square ) in the context of the problem.
( f(5)=square ), meaning that ( square ) seconds after the object was launched, the object was ( square ) feet above the ground. this interpretation ( square ) in the context of the problem.
based on the observations above, it is clear that an appropriate domain for the function is

Explanation:

Step1: Find when the object hits the ground ($f(x) = 0$)

Set $-16x^{2}+48x + 64=0$. Divide by $-16$: $x^{2}-3x - 4 = 0$. Factor: $(x - 4)(x+1)=0$. Solutions $x = 4$ or $x=-1$. Since time $x\geq0$, discard $x=-1$.

Step2: Determine the domain

The object is in the air from $x = 0$ (launch) to $x = 4$ (hit ground).

Answer:

The domain of the function is $0\leq x\leq4$.