Question

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A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t) = 120t - 16t^2 . After how long will it reach its maximum height?
Do not round your answer.

Answer 1

Answer: After 3.75 seconds

Explanation:

For a Quadratic function in the form
`f(x)=ax^2+bx+c`, if
`a<0` then the parabola opens downward.

Rewriting the given function as:

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

You can identify that
`a=-16`

Since
`a<0` the the parabola opens downward.

Therefore, we can conclude that the x-coordinate of the vertex is the time in seconds in which the ball will reach the maximum height. You can find it with this formula:

`t=(-b)/(2a)`

Substitute values, we get

`t=(-120)/(2(-16))=3.75\ seconds`