Use the table to answer the question.

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 linear function family
the linear function family

the quadratic function family
the quadratic function family

the square root function family
the square root function family

the cubic function family

Answer 1

To determine the type of function that best models the height of the flying disc over time, we can analyze the pattern of the height values given in the table.

The height values are as follows:

• At 8 seconds: 14.2 feet
• At 9 seconds: 14.55 feet
• At 10 seconds: 14.8 feet
• At 11 seconds: 14.95 feet
• At 12 seconds: 15.0 feet
• At 13 seconds: 14.95 feet

When we examine the heights, we can see that they increase at first, reach a peak at 12 seconds, and then begin to decrease at 13 seconds, resembling a parabolic shape rather than a straight line.

This pattern suggests that the height of the disc could be modeled by a quadratic function, which typically takes the form \( y = ax^2 + bx + c \). Quadratic functions can represent parabolic trajectories, which is characteristic of flying objects influenced by gravity.

Thus, the function family that best fits this data is the quadratic function family.

Response: the quadratic function family