Find a Power Function That Models the Data in the Table

question 101

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.

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Definitions:

Negative Relationship

A correlation where an increase in one variable leads to a decrease in another variable.

Vertical Axis

In a graph or chart, the vertical line or axis is typically used to represent the dependent variable or measure.

Horizontal Axis

In graphing, this is the x-axis, typically used to represent the independent variable or categories being compared.

Straight Line

A geometric figure formed by two points and extended infinitely in both directions.