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Quadratic models and feasible domains
Quadratic models and feasible domains
Example 1
A rectangle has width x and length 18−x metres. Its area is A(x)=x(18−x). Find A(5), in m2.
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Answer: 65
- A(5)=5×(18−5)=65m2.
Example 2
For a rectangle with sides x and 20−x, which domain gives two positive side lengths?
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Answer: 0<x<20
- Both x and 20−x must be positive. Hence 0<x<20.
Example 3
A ball's height is h(t)=−t2+14t, in metres. Apart from t=0, when is it at ground level?
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Answer: 14
- Set h=0 and factor: t(14−t)=0. The positive landing time is 14 seconds.
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