Question

Joseph jumped off of a cliff into the ocean in Miami while vacationing with some friends. His height as a function of time is given by () = −^ + + , where is the time in seconds and is the height in feet. Ow long did it take for Joseph to reach his maximum height? What was the highest point that Joseph reached? Joseph hit the water after how many seconds?

Answer 1

Explanation:

I think the missing equation in your question is: h(t) = -16
`t^(2)` + 16t + 480

Here is my answer:

As we know that the vertex form of a parabola, y=a
`(x-h)^(2)` + k where(h,k) is the vertex

h(t) = -16
`t^(2)` + 16t + 480

= -16 (
`t^(2) -t)` + 480

= -16
`(t-(1)/(2)) ^(2)` + 484

So the vertex is (
`(1)/(2)` , 484)

a. It take for Joseph
`(1)/(2)` second to reach his maximum height

b. The highest point that Joseph reached is the vertex of the function, it is 484 ft

c. Joseph hit the water after how many seconds?

<=> h(t) = 0

<=> -16
`t^(2)` + 16t + 480 = 0

<=> t =
`(192)/(32)` second = 6 sec

Hope it will find you well