Question

Use the table to answer the question. Time (seconds) 8 9 10 11 12 13 . . . Height (feet) 14.2 14.55 14.8 14.95 15.0 14.95 . . . Grace creates a table to track the approximate height reached by her flying disc, in feet, as a function of the time, in seconds, since she released the disc. Determine the type of function that best models the data. What function family does it belong to? (1 point) Responses the quadratic function family the quadratic function family the cubic function family the cubic function family the linear function family the linear function family the square root function family

Answer 1

To determine the type of function that best models the data, we need to analyze the pattern in the height values as time progresses.

From the given data:

• At 8 seconds, the height is 14.2 feet.
• At 9 seconds, the height is 14.55 feet.
• At 10 seconds, the height is 14.8 feet.
• At 11 seconds, the height is 14.95 feet.
• At 12 seconds, the height is 15.0 feet.
• At 13 seconds, the height is 14.95 feet.

Observations:

• The heights increase from 14.2 feet to 15.0 feet as time goes from 8 seconds to 12 seconds, which suggests that there is a maximum height reached (15.0 feet) before the height decreases slightly at 13 seconds to 14.95 feet.
• The increments in height are not consistent, indicating that the relationship is not linear.
• The increase in height values resembles a parabolic curve where the height increases to a maximum and then decreases.

Based on these observations, the function that best models this data is likely to be quadratic. Specifically, it seems to fit the shape of an inverted parabola due to the peak at 12 seconds.

Thus, the answer is: the quadratic function family.