Question

Question #05734

Answer 1

`5` feet

Explanation:

Take a look at the graph of this equation.
graph{-16x^2+8x+4 [-10, 10, -5, 5]}

We can see that the maximum height of the object occurs at the vertex of the parabola. In order to find the time `t_max` where the object reaches the vertex, we can use the following formula:
`t_max=-b/(2a)`

This is the formula used throughout algebra to find the `x`-coordinate of the vertex of a parabola.

In the equation `-16t^2+8t+4`, we have `a=-16` and `b=8`, so:
`t_max=-(8)/(2(-16))=1/4` seconds

This tells us that the maximum height of the object is reached at `t=1/4` seconds. However, the question asks for the actual height, not the time. To find the height, we simply plug in `1/4` for `t`:
`S(t)=-16t^2+8t+4`
`S_max(t)=S(t_max)=S(1/4)=-16(1/4)^2+8(1/4)+4`
`=5` feet