Question

A student tracks the height of a ball every second while it is in the air.

Some of the ordered pairs are shown in the table.


time,sec 0, 1, 2, 3
hight,ft 5, 53, 69, 53


Which type of function best models the student's data?

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(2 points)
Responses

linear increasing
linear increasing

linear decreasing
linear decreasing

quadratic concave up
quadratic concave up

quadratic concave down

Answer 1

To determine the type of function that best models the student's data based on the provided ordered pairs, we can analyze the height of the ball over time:

- At \( t = 0 \) seconds, the height is \( 5 \) feet.
- At \( t = 1 \) second, the height is \( 53 \) feet.
- At \( t = 2 \) seconds, the height is \( 69 \) feet.
- At \( t = 3 \) seconds, the height is \( 53 \) feet.

Analyzing the heights:
- From \( t = 0 \) to \( t = 1 \), the height increases significantly from \( 5 \) feet to \( 53 \) feet.
- From \( t = 1 \) to \( t = 2 \), the height increases further to \( 69 \) feet.
- However, from \( t = 2 \) to \( t = 3 \), the height decreases from \( 69 \) feet back down to \( 53 \) feet.

This pattern suggests that the height reaches a maximum point at \( t = 2 \) seconds and then begins to decrease.

Given that the height increases to a maximum and then decreases, this behavior is characteristic of a quadratic function that is concave down (it opens downwards) and has a vertex (maximum point) at \( t = 2 \).

Thus, the best option is:

**quadratic concave down**.