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 \( h(x) = -16x^2 + 100 \) represents the height of a dropped object over time \( x \) (in seconds). Time cannot be negative in this real - world context of an object being dropped (since \( x \) represents the number of seconds after the object was dropped).

Step2: Evaluate each option

• For \( x=-2.75 \): A negative value of time does not make sense in the context of an object being dropped (we measure time after the object is dropped, so time should be non - negative).
• For \( x = 0.25 \): This is a positive time value, and we can use the model to predict the height at 0.25 seconds after the object is dropped.
• For \( x=1.75 \): This is a positive time value, and the model can be used to predict the height at 1.75 seconds after the object is dropped.
• For \( x = 2.25 \): This is a positive time value, and the model can be used to predict the height at 2.25 seconds after the object is dropped.

Answer:

\(-2.75\) (because time cannot be negative in the context of an object being dropped, so the model does not make sense for \(x=-2.75\))