Question

A food packet is dropped from a helicopter and is modeled by the function f(x) = -12x2 + 19200. The graph below shows the height f(x), in feet, of the food packet at different times x, in seconds:
Use the graph to determine the reasonable domain of f(x) based on the context.

all real numbers

x ≤ 19200

-40 ≤ x ≤ 40

0 ≤ x ≤ 40

Answer 1

 For this case we have the following function:
 $f(x) = -12x^2 + 19200$
 When the food package is on the plane, we have that the height of the package is given by:
 $f (0) = -12 (0) ^ 2 + 19200$
 Rewriting we have:
 $f (0) = 0 + 19200 f (0) = 19200$
 When, time passes, the height decreases.
 When the time is 40 seconds (x = 40) the package reaches the ground and the height is 0.
 Therefore, a reasonable domain for the function is:
0 ≤ x ≤ 40
Answer:
0 ≤ x ≤ 40