Solve the Problem
-A Ball Is Tossed Upward $\mathrm { t }$

Solve the problem
-A ball is tossed upward. Its height after $\mathrm { t }$ seconds is given in the table.
$\begin{array}{l|rcrcr}\text { Time (seconds) } & 0.5 & 1 & 1.5 & 2 & 2.5 \\\hline \text { Height (feet) } & 26.5 & 39.5 & 44.5 & 41.5 & 30.5\end{array}$

Find a quadratic function to model the data. Use the model to determine when the ball reaches its maximum height, as well as the value of the maximum height.

A) The ball never reaches a maximum height.
B) The ball reaches a maximum height of $44.6$ feet in $1.6$ seconds.
C) The ball reaches a maximum height of 40 feet in $1.5$ seconds.
D) The ball reaches a maximum height of 50 feet in $2.1$ seconds.