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

Answer:

The maximum height reached by the baseball is 48 feet.

Step-by-step 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 $h=-\frac{b}{2a}$ and $k=f(h)$.

According to the given function, we have

$a=-10$ and $b=40$

$h=-\frac{40}{2(-10)}=\frac{40}{20}=2$

$k=f(2)=-10(2)^{2} +40(2)+8=-10(4)+80+8=-40+80+8=48$

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