Find a Power Function That Models the Data in the Table

Multiple Choice

Find a power function that models the data in the table. Round to three decimal places if necessary.
-A ball is tossed upward. Its height after t seconds is given in the table. $$\begin{array} { l | r r r r r } \text { Time (seconds) } & 0.5 & 1 & 1.5 & 2 & 2.5 \\\hline \text { Height (feet) } & 26.5 & 39.5 & 44.5 & 41.5 & 30.5\end{array}$$ 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 reaches a maximum height of 40 feet in 1.5 seconds.
B) The ball reaches a maximum height of 50 feet in 2.1 seconds.
C) The ball never reaches a maximum height.
D) The ball reaches a maximum height of 44.6 feet in 1.6 seconds.