Samantha is standing on top of a boulder at her neighborhood pond. She picks up a rock, so that it is 6 feet off the ground, and throws the rock into the pond. The height of the rock after t seconds can be modeled by the expression -16t^2 + 32t + 6. What does the 6 represent in the context of this problem?

Question

Responses

6 represents the number of rocks Samantha found at the pond.
6 represents the number of rocks Samantha found at the pond.

6 does not make sense as a value in this problem.
6 does not make sense as a value in this problem.

6 represents the height of the rock when Samantha throws it.
6 represents the height of the rock when Samantha throws it.

6 represents the number of seconds Samantha holds the rock before throwing it.

Answer 1

The correct response is:

6 represents the height of the rock when Samantha throws it.

In this context, the height of the rock is modeled by the expression \(-16t^2 + 32t + 6\), and the constant term \(6\) indicates the height (in feet) at which the rock is when \(t = 0\) seconds, which is 6 feet off the ground.