Question

A baseball is hit, and rises to a height above the ground, f(t), in feet, at time t, in seconds, can be estimated by the formula: f(t)=-10t^(2)+40t+8

Answer 1

The maximum height reached by the baseball is 48 feet.

Explanation:

The given function is

`f(t)=-10t^(2)+40t+8`

To find the maximum height reached by the ball, we need to find the vertex of the parabolla represented by the given quadratic equation.

Remember that a vertex has coordinates (h,k), where
`h=-(b)/(2a)` and
`k=f(h)`.

According to the given function, we have

`a=-10` and
`b=40`

`h=-(40)/(2(-10))=(40)/(20)=2`

`k=f(2)=-10(2)^(2) +40(2)+8=-10(4)+80+8=-40+80+8=48`

So, the vertex has coordinates of (2,48), which means the maximum height reached by the baseball is 48 feet.