document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=930356>Question 930356</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a. Write a quadratic function to represent to area of all rectangles with a perimeter of 36 feet.\r<BR>\n" );
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document.write( "b. What is the vertex?\r<BR>\n" );
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document.write( "c. How can the graph of your function and the vertex help you determine which rectangle has the area? What are the side lengths for the rectangle with the greatest area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #564974 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=564974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2%28L%2BW%29=36 ALIGN=MIDDLE  ALT=\"P=2%28L%2BW%29=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2BW=18 ALIGN=MIDDLE  ALT=\"L%2BW=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=18-W ALIGN=MIDDLE  ALT=\"L=18-W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW ALIGN=MIDDLE  ALT=\"A=L%2AW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%2818-W%29W ALIGN=MIDDLE  ALT=\"A=%2818-W%29W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=18W-W%5E2 ALIGN=MIDDLE  ALT=\"A=18W-W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-%28W%5E2-18W%2B81%29%2B81 ALIGN=MIDDLE  ALT=\"A=-%28W%5E2-18W%2B81%29%2B81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-%28W-9%29%5E2%2B81 ALIGN=MIDDLE  ALT=\"A=-%28W-9%29%5E2%2B81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81 ALIGN=MIDDLE  ALT=\"81\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
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document.write( "The graph isn't really required only the vertex form of the equation.<BR>\n" );
document.write( "Since there is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiplier in front of the quadratic term, the parabola opens downwards so the vertex value is the maximum. <BR>\n" );
document.write( "So you know the width (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=9 ALIGN=MIDDLE  ALT=\"W=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >) at the maximum area (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=81 ALIGN=MIDDLE  ALT=\"A=81\"   DISABLED_style= \"max-width:90%; height:auto;\" >). <BR>\n" );
document.write( "Then you also know the length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=18-W=18-9=9 ALIGN=MIDDLE  ALT=\"L=18-W=18-9=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So the maximum area rectangle is a square.<BR>\n" );
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