Question

Please help me with this problem

Answer 1

`0 \le t \le 3`

Explanation:

`h(t)` is a quadratic function centered around the origin, with zeros at (-3, 0) and (3, 0) (which you can find by solving
`h(t) = -16t^2 + 144 = 0`, i.e.
`t^2 = 9`, so
`t = 3` and
`t = -3`).

Given that the function curves downward at its peak,
`h(t)` is positive for
`-3 \le t \le 3`. If the value of the function is negative, the ball would be under the ground, which does not make sense. Also, a negative value of time does not make sense in the context of this problem. So we restrict t to be positive. This means that the only valid domain where t is positive and the value of the function is at least 0 is
`0 \le t \le 3`