document.write( "Question 371028: THE NUMBER OF TICKETS SOLD EACH DAY FOR AN UP COMING PERFORMANCE OF HANDLES IS GIVEN BY N(X)= -0.4X^2 +8.8X +15, WHERE X IS THE NUMBER OF DAYS SCINSE THE CONCERT WAS FIRST ANNOUNCED. WHEN WILL DAILY TICKET SALES PEAK? ALSO, HOW MANY TICKETS WILL BE SOLD THAT DAY? \n" ); document.write( "

Algebra.Com's Answer #264874 by jsmallt9(3758) $\"\"$ $\"About$

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$\"N%28x%29=+-0.4x%5E2+%2B8.8x+%2B15\"$
\n" ); document.write( "The easy way to solve this is based on understanding that the graph of N(x) is a parabola. And not only is it a parabola, it is a parabola that opens downward (because of the minus in front of the squared term and because the squared term is x (and not y)).\n" ); document.write( "Once we imagine a picture of a parabola that opens downward, we should realize that the maximum (highest) point will be the vertex of that parabola. So allwe have to do is figure out the vertex.

\n" ); document.write( "The quick way to find a vertex is to use $\"x+=+%28-b%29%2F%282a%29\"$ where the \"a\" and \"b\" come from the general equation of quadratic equations: $\"y+=+ax%5E2+%2Bbx+%2Bc\"$ . Using this on N(x) we get:
\n" ); document.write( " $\"x+=+%28-8.8%29%2F%282%2A%28-0.4%29%29+=+%28-8.8%29%2F%28-0.8%29+=+11\"$
\n" ); document.write( "So 11 days after the announcement, the ticket sales will be at a peak. And N(11) will tell us how many tickets were sold on that day:
\n" ); document.write( " $\"N%2811%29+=+-0.4%2811%29%5E2+%2B8.8%2811%29+%2B15\"$
\n" ); document.write( "Simplifying...
\n" ); document.write( " $\"N%2811%29+=+-0.4%28121%29+%2B8.8%2811%29+%2B15\"$
\n" ); document.write( " $\"N%2811%29+=+-48.4+%2B+96.8+%2B15\"$
\n" ); document.write( " $\"N%2811%29+=+63.4\"$
\n" ); document.write( "So approximately 63 tickets were sold 11 days after the announcement of the concert. \n" ); document.write( "

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