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.

Question

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.

Quizplus · Accepted Answer

Given the data, a quadratic function best models the trajectory of a tossed ball, which naturally follows a parabolic path due to gravity. The maximum height is reached at the vertex of the parabola. The data suggests the ball reaches its peak height between 1.5 and 2 seconds, with the height values increasing up to 44.5 feet at 1.5 seconds and then decreasing. Thus, the closest match to the data provided is an estimated maximum height of 44.6 feet at around 1.6 seconds, indicating the vertex of the parabola is near these values.

Find a Power Function That Models the Data in the Table