document.write( "Question 335717: The number of tickets sold each day for an up coming performance of Handel's Messiah is given by N(x)=-0.4x^2+8.8x+12, where x is the number of days since the concert was 1st announced. When will the daily tickets sales peak and how many tickets will be sold that day? \n" ); document.write( "

Algebra.Com's Answer #240839 by jsmallt9(3758) $\"\"$ $\"About$

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$\"N%28x%29=-0.4x%5E2%2B8.8x%2B12\"$
\n" ); document.write( "Because of the $\"x%5E2\"$ term this is a parabola. And since the coefficient of the $\"x%5E2\"$ term is negative the parabola opens downward. For a downward opening parabola, the maximum value will be at the vertex.

\n" ); document.write( "The x coordinate of the vertex for any vertically oriented parabola is $\"%28-b%29%2F2a\"$ . So the x coordinate of this parabola is:
\n" ); document.write( " $\"x+=+%28-b%29%2F2a+=+%28-8.8%29%2F2%28-0.4%29+=+%28-8.8%29%2F%28-0.8%29+=+11\"$

\n" ); document.write( "So the maximum number of tickets will be sold 11 days after the announcement of the concert. The number of tickets sold on that day is:
\n" ); document.write( " $\"N%2811%29+=+-0.4%2811%29%5E2+%2B+8.8%2811%29+%2B+12\"$
\n" ); document.write( " $\"N%2811%29+=+-0.4%28121%29+%2B+8.8%2811%29+%2B+12\"$
\n" ); document.write( " $\"N%2811%29+=+-48.4+%2B+96.8+%2B+12\"$
\n" ); document.write( " $\"N%2811%29+=+60.4\"$
\n" ); document.write( "So there will be approximately 60 tickets sold that day. \n" ); document.write( "

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