Relate the domain of a quadratic function to its graph and situation.
Find the meaningful domain of a quadratic model in context
Problem
What is the meaningful domain for the revenue or profit model \(R(p)=p(40-p)\) if it represents price \(p\) and demand \(40-p\) must be nonnegative?
Big Picture
What this problem is really about
The factors in a contextual quadratic can represent quantities that each impose their own input constraint. We’ll name those quantities, require both to remain nonnegative, solve each inequality with sign changes handled carefully, and intersect the conditions while checking the boundary meanings.
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