document.write( "Question 533657: this is a word problom from my college algebra I book that deals with Inverse Functions: \"John owns a hotdog stand. He has found that his profit is represented by the equation P=-x^2+56x+77, with P being profits and x the number of hotdogs. How many hotdogs must he sell to earn the most profit? What will be his maximum profit?\" \n" ); document.write( "

Algebra.Com's Answer #351111 by Earlsdon(6294) $\"\"$ $\"About$

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$\"P+=+-x%5E2%2B56x%2B77\"$ This is a quadratic equation which, when graph, will give a parabola that opens downward. (Note the negative $\"x%5E2\"$ term)
\n" ); document.write( "The x-coordinate of the maximum of this parabola, and thus the maximum number of hotdogs, is given by:
\n" ); document.write( " $\"x+=+-b%2F2a\"$ where: a = -1 and b = 56, so...
\n" ); document.write( " $\"x+=+-56%2F2%28-1%29\"$
\n" ); document.write( " $\"x+=+28\"$
\n" ); document.write( "John must sell 28 hotdogs to earn the most profit.
\n" ); document.write( "The maximum profit, $\"P%5Bm%5D\"$ , can be found by substituting $\"x+=+28\"$ into the given equation for profit.
\n" ); document.write( " $\"P%5Bm%5D+=+-%2828%29%5E2%2B56%2828%29%2B77\"$
\n" ); document.write( " $\"P+=+861\"$ \n" ); document.write( "

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