An object was launched off the top of a building. The function f, of, x, equals, minus, 16, x, squared, plus, 48, x, plus, 64f(x)=−16x
2
+48x+64 represents the height of the object above the ground, in feet, xx seconds after being launched. Find and interpret the given function values and determine an appropriate domain for the function.
Answer
Attempt 1 out of 2
f, of, minus, 1, equalsf(−1)=
, meaning that
seconds after the object was launched, the object was
feet above the ground. This interpretation
makes sense
in the context of the problem.
f, of, 0, point, 5, equalsf(0.5)=
, meaning that
seconds after the object was launched, the object was
feet above the ground. This interpretation
makes sense
in the context of the problem.
f, of, 5, equalsf(5)=
, meaning that
seconds after the object was launched, the object was
feet above the ground. This interpretation
does NOT make sense
in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is
non-negative real numbers
.
f(-1) = -16(-1)^2 + 48(-1) + 64 = -16 + (-48) + 64 = 0
Therefore, f(-1) = 0, meaning that 1 second after the object was launched, the object was 0 feet above the ground. This interpretation makes sense in the context of the problem.
f(0.5) = -16(0.5)^2 + 48(0.5) + 64 = -16(0.25) + 24 + 64 = -4 + 24 + 64 = 84
Therefore, f(0.5) = 84, meaning that 0.5 seconds after the object was launched, the object was 84 feet above the ground. This interpretation makes sense in the context of the problem.
f(5) = -16(5)^2 + 48(5) + 64 = -16(25) + 240 + 64 = -400 + 240 + 64 = -96
Therefore, f(5) = -96, meaning that 5 seconds after the object was launched, the object was -96 feet above the ground. This interpretation does NOT make sense in the context of the problem, as height cannot be negative.
Based on the observations above, it is clear that an appropriate domain for the function is non-negative real numbers.