document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159089>Question 159089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into three plots with two fences parallel to one of the sides. What is the area that can be enclosed? I need to find the vertex but cannot figure out how to solve this problem. (Analyzing Graphs of Quadratic Functions). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117204 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=117204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A farmer with 10,000 meters of fencing wants to enclose a rectangular field and<BR>\n" );
document.write( " then divide it into three plots with two fences parallel to one of the sides.<BR>\n" );
document.write( " What is the area that can be enclosed? I need to find the vertex<BR>\n" );
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document.write( "They want to find the max area that can be enclosed which is the vertex<BR>\n" );
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document.write( "Since they want three plots, we will have two lengths and four widths<BR>\n" );
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document.write( "Let L = length, Let x = the width<BR>\n" );
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document.write( "2L + 4x = 10000<BR>\n" );
document.write( "Simplify divide by 2<BR>\n" );
document.write( "L + 2x = 5000<BR>\n" );
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document.write( "L = (5000 - 2x)<BR>\n" );
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document.write( "Area = L*x<BR>\n" );
document.write( "Substitute (5000-2x) for L<BR>\n" );
document.write( "A = (5000-2x) * x<BR>\n" );
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document.write( "A quadratic equation<BR>\n" );
document.write( "A = -2x^2 + 5000x<BR>\n" );
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document.write( "When you want to find the vertex, you don't want to simplify the equation<BR>\n" );
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document.write( "To find the vertex, find the axis of symmetry; x = -b/(2a): a=-2, b=5000<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5000%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"%28-5000%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5000%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"%28-5000%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +1250 meters is the width for max area<BR>\n" );
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document.write( "Find the max area, substitute 1250 for x in the area equation:<BR>\n" );
document.write( "A = -2(1250^2) + 5000(1250)<BR>\n" );
document.write( "A = -3125000 + 6250000<BR>\n" );
document.write( "A = 3,125,000 sq meters is the max area<BR>\n" );
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document.write( "The vertex: 1250, 3,125,000<BR>\n" );
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document.write( "Did this make sense to you? Any questions? </SPAN>\n" );
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