Question

Which explanation provides the best real-world scenario of the graph?

-If an object is dropped from a height of 120 feet, the function h(t) = –16t2 – 120 gives the height of the object after t seconds.

-If an object is dropped from a height of –16 feet, the function h(t) = –16t2 + 120 gives the height of the object after t seconds.

-If an object is dropped from a height of 120 feet, the function h(t) = –16t2 + 120 gives the height of the object after t seconds.

Answer 1

The last one is the only one that makes sense according to the standard position function. -16t^2 is the pull of gravity on an object in free fall, and the height is 120 feet above the ground. Hopefully that's what you need since there's no graph we can refer to

Answer 2

The explanation that best provides the real-world scenario is:

If an object is dropped from a height of 120 feet, the function

`h(t)=-16t^2+120`

gives the height of the object after t seconds.

Explanation:

a)

If an object is dropped from a height of 120 feet, the function
`h(t)=-16t^2-120` gives the height of the object after t seconds.

This option is incorrect.

Since when t=0 we have:

h(t)= -120

This is not possible as the object is above the ground and hence must have positive height initially.

b)

If an object is dropped from a height of -16 feet, the function
`h(t)=-16t^2+120` gives the height of the object after t seconds.

This option is incorrect.

Since a object when is dropped from some height then it must be a positive height.

Also, when t=0 we have: h(t)= 120 feet.

This means that the object is dropped from a height of 120 feet.

c)

If an object is dropped from a height of 120 feet, the function
`h(t)=-16t^2+120` gives the height of the object after t seconds.

In this when t=0 we have:

h(t)=120 that means the height of the object initially was 120 feet and then it decreases with the increase in time as the object will reach the ground with the time increase and hence height will decrease.

Hence, this option is correct.