Question

the table shows the approximate height of an object x seconds after the object was dropped. the function h(x) = -16x² + 100 models the data in the table.
height of a dropped object

time (seconds)	height (feet)
0.5	96
1	84
1.5	65
2	37

for which value of x would this model make the least sense to use?
-2.75
0.25
1.75
2.25

Explanation:

Step1: Analyze the context

The model is about the height of a dropped object over time (x seconds). Time cannot be negative in this real - world context of an object being dropped (we start timing when the object is dropped, so x should be non - negative).

Step2: Evaluate each option

• For \(x = 0.25\): This is a positive time value, and in the context of a dropped object, it makes sense to use the model to find the height at 0.25 seconds after dropping.
• For \(x=1.75\): This is a positive time value, and we can use the model to find the height at 1.75 seconds after dropping.
• For \(x = 2.25\): This is a positive time value, and we can use the model to find the height at 2.25 seconds after dropping.
• For \(x=- 2.75\): Time cannot be negative in the context of an object being dropped (we measure the time elapsed since the object was dropped, so negative time has no physical meaning here). So the model makes the least sense to use when \(x=-2.75\).

Answer:

\(-2.75\) (the option corresponding to - 2.75, which is the first option in the list of choices)