document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121157>Question 1121157</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of tickets sold each day for an upcoming performance of&#8203; Handel's Messiah is given by Upper N left parenthesis x right parenthesis equals negative 0.6 x squared plus 14.4 x plus 14&#8203;, 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&#8203; day? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736931 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula looks like:\r<BR>\n" );
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document.write( "N(x) = -.6x^2 + 14.4x + 14\r<BR>\n" );
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document.write( "N is the function name.<BR>\n" );
document.write( "x is the argument of the function.<BR>\n" );
document.write( "the expression on the right is the formula of the function.\r<BR>\n" );
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document.write( "you could replace N(x) with y and the function would read:\r<BR>\n" );
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document.write( "y = -.6x^2 + 14.4x + 14\r<BR>\n" );
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document.write( "you can graph the equation in this form.\r<BR>\n" );
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document.write( "the graph would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/081101.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "you can see from the graph that the maximum value of y (also called N(x)) is 100.4 when x = 12.\r<BR>\n" );
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document.write( "this can also be found by formula.\r<BR>\n" );
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document.write( "the formula is x = -b/2a.\r<BR>\n" );
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document.write( "the equation has to be in standard form of y = ax^2 + bx + c.\r<BR>\n" );
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document.write( "it's already in that form.\r<BR>\n" );
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document.write( "y = -.6x^2 + 14.4x + 14 gets you:\r<BR>\n" );
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document.write( "a = -.6<BR>\n" );
document.write( "b = 14.4<BR>\n" );
document.write( "c = 14\r<BR>\n" );
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document.write( "x = -b/2a gets you x = 14.4 / -1.2\r<BR>\n" );
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document.write( "this results in x = 12.\r<BR>\n" );
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document.write( "when x = 12, the function of y = -.6x^2 + 14.4x + 14 becomes y = -.6 * 12^2 + 14.4 * 12 + 14 which becomes y = 100.4\r<BR>\n" );
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document.write( "when x is 12, y is 100.4\r<BR>\n" );
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document.write( "x represents the number of days since the concert was first announced.\r<BR>\n" );
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document.write( "y represents the number of tickets sold each day.\r<BR>\n" );
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document.write( "here's a reference on functional notation.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://mathbitsnotebook.com/Algebra1/Functions/FNNotationEvaluation.html\" target = \"_blank\">https://mathbitsnotebook.com/Algebra1/Functions/FNNotationEvaluation.html</a>\r<BR>\n" );
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document.write( "here's another reference on functional notation.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/fcnnot.htm\" target = \"_blank\">https://www.purplemath.com/modules/fcnnot.htm</a>\r<BR>\n" );
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document.write( "here's a reference on quadratic equations.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.cliffsnotes.com/study-guides/algebra/algebra-i/quadratic-equations/solving-quadratic-equations\" target = \"_blank\">https://www.cliffsnotes.com/study-guides/algebra/algebra-i/quadratic-equations/solving-quadratic-equations</a>\r<BR>\n" );
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document.write( "lots more on how to solve quadratic equations from purplemath.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.google.com/search?q=quadratic+equations+purplemath&oq=quadratic+equations+purplemath&aqs=chrome.0.69i59j69i60j0l4.7671j1j7&sourceid=chrome&ie=UTF-8\" target = \"_blank\">https://www.google.com/search?q=quadratic+equations+purplemath&oq=quadratic+equations+purplemath&aqs=chrome.0.69i59j69i60j0l4.7671j1j7&sourceid=chrome&ie=UTF-8</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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