Question

A baseball is hit into the​ air, and its height h in feet after t seconds is given by h(t)= -16t^2+128t+2. The height of the baseball when it is hit is ? The baseball reaches its maximum height after ? The maximum height of the baseball is ?

Answer 1

`\large \boxed{\sf \ \text{2 feet, 4 seconds, 258 feet } \ }`

Explanation:

Hello,

To know the height of the baseball when it is hit we have to compute h(0), as t = 0 is when the baseball is hit into the air.

`h(0)=-16\cdot 0^2+128 \cdot 0+2=2`

So, the answer is 2 feet.

h(x) is a parabola which can be written as
`ax^2+bx+c`, it means that the vertex is the point (-b/2a,h(-b/2a)).

The baseball reached its maximum height after

`(-b)/(2a)=(-128)/(-2*16)=\boxed{4 \text{ seconds}}`

And the maximum height of the baseball is h(4).

`h(0)=-16\cdot 4^2+128 \cdot 4+2=-256+512+2=\boxed{258 \ \text{feet}}`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you