document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028396>Question 1028396</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi I have a word problem with a linear equation of f(x)=-0.002x^2+1.4x-400. X is the number of pretzels sold, and I was told to find a max profit. How would I start this equation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643481 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=643481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is a quadratic equation.\r<BR>\n" );
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document.write( "set the equation equal to 0 and you get -.002x^2 + 1.4x - 400 = 0\r<BR>\n" );
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document.write( "the equation is now in standard quadratic equation form of ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "a is the coefficient of the x^2 term which is -.002<BR>\n" );
document.write( "b is the coefficient of the x term which is 1.4<BR>\n" );
document.write( "c is the constant term which is -400\r<BR>\n" );
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document.write( "the x-coordinate of max/min point of a quadratic equation can be found using the following formula:\r<BR>\n" );
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document.write( "x = -b/2a.\r<BR>\n" );
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document.write( "in your problem, this becomes x = -1.4 / (2*(-.002)) which becomes -1.4 / -.004 which results in x = 350.\r<BR>\n" );
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document.write( "when x = 350, the equation of f(x) = -.002x^2 + 1.4x - 400 becomes f(350) = -.002 * (350^2 + 1.4 * 350 - 400 which results in f(350) = -155.\r<BR>\n" );
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document.write( "that's a negative number which indicates that you didn't make a profit, but took a loss, with the minimum loss occurring when you sold 350 pretzels.\r<BR>\n" );
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document.write( "this assumes that f(x) is supposed to represent your profit.\r<BR>\n" );
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document.write( "the graph of your equation is shown below.\r<BR>\n" );
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document.write( "this graph confirms the manual calculation using the max/min formula.\r<BR>\n" );
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document.write( "when the coefficient of the x^2 term of a quadratic equation is negative, the max/min formula give you the max.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/040601.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "in the graph, y means the same thing as f(x).\r<BR>\n" );
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document.write( "the x-axis tells you the number of pretzels sold.<BR>\n" );
document.write( "the y-axis tells you the result of the equation using that value of x.\r<BR>\n" );
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document.write( "if f(x) is supposed to represent your profit, then you didn't make any profit, but took a loss instead.\r<BR>\n" );
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document.write( "you can say that your maximum profit is when 350 pretzels are sold.\r<BR>\n" );
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document.write( "you can say that your maximum profit is -155.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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