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Question

The amount of money a certain company makes can be represented by the graph y=x^2-8x-33, where x is the quantity produced. What is the smallest quantity at which the company can produce to break even or make a profit?

Accepted Answer

First we factor x^2-8x-33 into (x-11)(x+3). So, y=0 at x=-3 or x=11. The quantity produced must be a positive amount, so that means the company breaks even (making no money) at x=11 and begins to make a profit after that point (y>0).