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

Answer:

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

Step-by-step 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

   $\dfrac{-b}{2a}=\dfrac{-128}{-2*16}=\boxed{4 \text{ seconds}}$

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