Learning Resources

Home »  » Courses » Mathematics » Advanced Mathematics 3207 (delisted) » Unit 02 » Set 01 ILO 02 » Step F

Investigation 2: Whale-watching Tours

Step F

Analyze the graph of the new function and compare it to the linear functions you have already graphed in steps B and D. Note: this new function, h(x), is a quadratic since it is the combination of two linear functions. The graph is shaped like a parabola and has a maximum value (IE: a maximum profit). 

The domain is 

{x / x ? R}. 

However within the context of the problem, this domain won't work. Recall in step D you found that the tour couldn't have more than 40 extra passengers. Hence the domain, within the context of the problem, is

The range, which represents the total revenue, can be found by locating the vertex. The y-coordinate of the vertex will be the greatest revenue possible. Note also that the lowest possible revenue will be $0. You should now be able to find the range.