document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132300>Question 132300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help.\r<BR>\n" );
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document.write( "The number of tickets sold each day for a performance is given by N(x)=-0.5x^2+10x+13, 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?\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96653 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=96653\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember, the peak occurs at the vertex. \r<BR>\n" );
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document.write( "To find the vertex, we first need to find the axis of symmetry (ie the x-coordinate of the vertex)\r<BR>\n" );
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document.write( "To find the axis of symmetry, use this formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.5x%5E2%2B10x%2B13 ALIGN=MIDDLE  ALT=\"y=-0.5x%5E2%2B10x%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that a=-0.5 and b=10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-10%29%2F%282%2A-0.5%29 ALIGN=MIDDLE  ALT=\"x=%28-10%29%2F%282%2A-0.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=10 and a=-0.5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-10%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"x=%28-10%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -0.5 to get -1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So the axis of symmetry is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the x-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Lets plug this into the equation to find the y-coordinate of the vertex.\r<BR>\n" );
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document.write( "Lets evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2810%29 ALIGN=MIDDLE  ALT=\"f%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-0.5x%5E2%2B10x%2B13 ALIGN=MIDDLE  ALT=\"f%28x%29=-0.5x%5E2%2B10x%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2810%29=-0.5%2810%29%5E2%2B10%2810%29%2B13 ALIGN=MIDDLE  ALT=\"f%2810%29=-0.5%2810%29%5E2%2B10%2810%29%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2810%29=-0.5%2A100%2B10%2A10%2B13 ALIGN=MIDDLE  ALT=\"f%2810%29=-0.5%2A100%2B10%2A10%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 10 to the 2nd power to get 100\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2810%29=-50%2B10%2A10%2B13 ALIGN=MIDDLE  ALT=\"f%2810%29=-50%2B10%2A10%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -.5 and 100 to get -50\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2810%29=-50-100%2B13 ALIGN=MIDDLE  ALT=\"f%2810%29=-50-100%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 10 and 10 to get 100\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2810%29=50%2B13 ALIGN=MIDDLE  ALT=\"f%2810%29=50%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add -50 and 100 to get 50\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2810%29=63 ALIGN=MIDDLE  ALT=\"f%2810%29=63\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 50 and 13 to get 63\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=63 ALIGN=MIDDLE  ALT=\"y=63\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the vertex is (10,63)\r<BR>\n" );
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document.write( "So on the 10th day, the tickets sales will peak at 63<BR>\n" );
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