The domain of the quadratic equation is all non-negative real numbers.
How to analyze and interpret a quadratic equation according to a physical phenomenon
The picture indicates the case of the launch of an object from the top of a building. The height of the object (f(x)), in feet, as a function of time, (x), in seconds. Both height and time are represented by non-negative real numbers and hence the following solutions do not make sense in the context of problem:
- x < 0
- x > 0, f(x) < 0
Now we proceed to fill the blanks in the four paragraphs:
f(- 2) = 0, meaning that - 2 second after the object was launched, the object was 0 feet above the ground. This interpretation does NOT make sense in the context of the problem.
f(0.5) = 100, meaning that 0.5 seconds after the object was launched, the object was 100 feet above the ground. This interpretation make sense in the context of the problem.
f(6) = - 224, meaning that 6 seconds after the object was launched, the object was - 224 feet above the ground. This interpretation does NOT make sense in the context of the problem.
Based on the observation above, it is clear that an approximate domain for the function is all non-negative real numbers.
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