document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=668721>Question 668721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with setting up the function. Thanks.<BR>\n" );
document.write( "A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 328 feet of fencing and doesn’t fence the side along the street, what is the largest area that can be enclosed?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #415826 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=415826\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is like fencing in a rectangle, then removing one side<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the area enclosed<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the side parallel to the street<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the length of a side perpendicular to the street<BR>\n" );
document.write( "The amount of fencing is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+%2B+2x+ ALIGN=MIDDLE  ALT=\"+y+%2B+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+%2B+2x+=+328+ ALIGN=MIDDLE  ALT=\"+y+%2B+2x+=+328+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area enclosed is <BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+x%2Ay+ ALIGN=MIDDLE  ALT=\"+A+=+x%2Ay+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+328+-+2x+ ALIGN=MIDDLE  ALT=\"+y+=+328+-+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+x%2A%28+328+-+2x+%29+ ALIGN=MIDDLE  ALT=\"+A+=+x%2A%28+328+-+2x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-2x%5E2+%2B+328x+ ALIGN=MIDDLE  ALT=\"+A+=+-2x%5E2+%2B+328x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Because of the minus sign in front of the squared term, the equation<BR>\n" );
document.write( "has a maximum and not a minimum<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+x%2A%28+-2x+%2B+328+%29+ ALIGN=MIDDLE  ALT=\"+A+=+x%2A%28+-2x+%2B+328+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum occurs halfway between the 2 roots<BR>\n" );
document.write( "One root is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+0+ ALIGN=MIDDLE  ALT=\"+x+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and to find the other root,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2x+%2B+328+=+0+ ALIGN=MIDDLE  ALT=\"+-2x+%2B+328+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+=+328+ ALIGN=MIDDLE  ALT=\"+2x+=+328+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+164+ ALIGN=MIDDLE  ALT=\"+x+=+164+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Half way between is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+82+ ALIGN=MIDDLE  ALT=\"+x+=+82+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+328+-+2x+ ALIGN=MIDDLE  ALT=\"+y+=+328+-+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+328+-+2%2A82+ ALIGN=MIDDLE  ALT=\"+y+=+328+-+2%2A82+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+328+-+164+ ALIGN=MIDDLE  ALT=\"+y+=+328+-+164+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+164+ ALIGN=MIDDLE  ALT=\"+y+=+164+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, at the maximum,<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+x%2Ay+ ALIGN=MIDDLE  ALT=\"+A+=+x%2Ay+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+82%2A164+ ALIGN=MIDDLE  ALT=\"+A+=+82%2A164+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+13448+ ALIGN=MIDDLE  ALT=\"+A+=+13448+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft2<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Here's the plot with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the vertical axis<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the horizontal axis<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-50%2C+200%2C+-3000%2C+15000%2C+-2x%5E2+%2B+328x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-50%2C+200%2C+-3000%2C+15000%2C+-2x%5E2+%2B+328x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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