Question

A rock is thrown into the air. The height (in feet) of the rock after t seconds is given by `h(t)=-16t^2+64t`. A. What is the height reached by the ball after 1 second? B. Determine the maximum height the rock attains

Answer 1

It reaches a height of 48 feet after 1 second
The maximum height (the h-value of the vertex of the equation) is 64 ft

Explanation:

Plug in 1 for `t` (since `t` represents time in seconds) to get `h(t)`, the height

`h(1)=-16*1^2+64*1`

`h(1)=-16*1+64`

`h(1)=-16+64`

`h(1)=48`

After 1 second, the rock reaches a height of 48 ft.

The maximum/minimum value of a quadratic equation is its vertex. If the quadratic equation opens down (as it does here), it will have a maximum value.

To find vertex of an equation in standard form: `(-b/(2a), f(-b/(2a)))`

Equation in standard form: `h(t)=at^2+bt+ct`

`a` in this case would be -16 and `b` would be 64:

`(-64)/(2*-16)=(-64)/(-32)=2`

Now plug 2 into the equation:

`h(2)=-16*2^2+64*2`

`h(2)=-16*4+64*2`

`h(2)=-64+128`

`h(2)=64`

The maximum height is 64 ft