document.write( "Question 1200637: The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N=−0.5x2+13x+12, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day?
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Algebra.Com's Answer #834831 by ikleyn(52855) $\"\"$ $\"About$

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\n" ); document.write( "The number of tickets sold each day for an upcoming performance of Handel's Messiah
\n" ); document.write( "is given by N=−0.5x2+13x+12, where x is the number of days since the concert
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document.write( "The given function N(x) = −0.5x^2 + 13x + 12  is a parabola opened downward.\r\n" );
document.write( "It has a maximum.\r\n" );
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document.write( "Its optimal value of x can be found using the formula   = ,\r\n" );
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document.write( "where \"a\" is the coefficient at x^2 and \"b\" is the coefficient at x.\r\n" );
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document.write( "In our case, a= -0.5,  b= 13,  so   =  =  = 13.\r\n" );
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document.write( "To find the maximum value of the function, substitute x= 13 into the formula N(x)\r\n" );
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document.write( "    N(13) = -0.5*13^2 + 13*13 + 12 = 96.5.\r\n" );
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document.write( "At this point, turn on your attention: the number of tickets must be integer number, \r\n" );
document.write( "but we got a non-integer value.\r\n" );
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document.write( "At this point, turn on your common sense and consider another integer argument in vicinity of 13,\r\n" );
document.write( "which, possible, will give you integer number of N(x).\r\n" );
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document.write( "Try x= 12. You will have  \r\n" );
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document.write( "    N(12) = -0.5*12^2 + 13*12 + 12 = 96.\r\n" );
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document.write( "It is just much better and more reasonable.\r\n" );
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document.write( "So, the answer is: the daily ticket sales peak is 96 tickets on 12-th day.\r\n" );
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document.write( "Notice, that the other possible answer is 96 tickets on 14-th day, too.\r\n" );
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\n" ); document.write( "\n" ); document.write( "So, the solution is a standard algebraic procedure, but we should turn on our common sense
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\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic function see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the vertex of a parabola\r
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\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.\r
\n" ); document.write( "\n" ); document.write( "Learn the subject from there once and for all.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Finding minimum/maximum of quadratic functions\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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