document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012465>Question 1012465</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABCD is a square of unit length. Points E and F are on the sides AB and AD respectively such that AE = AF = x. <BR>\n" );
document.write( "Show that the area 'y' of the quadrilateral CDFE is given by y = 1/2 (1 + x - x^2). What is the quadrilaterals greatest possible area. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628426 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52856)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=628426\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "ABCD is a square of unit length. Points E and F are on the sides AB and AD respectively such that AE = AF = x. <BR>\n" );
document.write( "Show that the area 'y' of the quadrilateral CDFE is given by y = 1/2 (1 + x - x^2). What is the quadrilaterals greatest possible area.<BR>\n" );
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document.write( "Hello, &nbsp;I am slightly surprised.\r<BR>\n" );
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document.write( "In my opinion, &nbsp;the area of the quadrilateral &nbsp;CDFE&nbsp; is &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F2 ALIGN=MIDDLE  ALT=\"x%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;and it is not the same as your formula &nbsp;&nbsp;y = 1/2 (1 + x - x^2).\r<BR>\n" );
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document.write( "For the proof that they are not the same, &nbsp;I prepared this plot.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+330%2C+330%2C+-2.5%2C+3.5%2C+-2.5%2C+3.5%2C%0D%0A++++++++++1+-+x%5E2%2F2%2C+0.5%2A%281%2Bx-x%5E2%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<B>Figure</B>. y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F2 ALIGN=MIDDLE  ALT=\"x%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5%2A%281%2Bx-x%5E2%29 ALIGN=MIDDLE  ALT=\"0.5%2A%281%2Bx-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green)\r<BR>\n" );
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document.write( "  </TD>\r\n" );
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document.write( "</TABLE> </SPAN>\n" );
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