Problem

Prepare complete restricted-domain sketch data for \(R(p)=p(20-p)\) on \(0\le~p\le~20\). Find the endpoint intercepts, midpoint axis, vertex value, opening, monotonic intervals, and range, and explain how these features determine the graph.

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Domain [0,20]; vertex (10,100); endpoints (0,0) and (20,0); increasing on [0,10], decreasing on [10,20]; range (−∞,100].

Domain [0,20]; vertex (10,−100); endpoints (0,0) and (20,0); decreasing on [0,10], increasing on [10,20]; range [−100,0].

Domain [0,20]; vertex (10,100); endpoints (0,0) and (20,0); increasing on [0,10], decreasing on [10,20]; range [0,100].

Domain [0,20]; vertex (10,100); endpoints (0,20) and (20,0); increasing on [0,10], decreasing on [10,20]; range [0,100].

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