document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=817049>Question 817049</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Studying quadratic equations. Can you help with an equation for this word problem? \r<BR>\n" );
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document.write( "Laura wants to plant a rectangular garden next to her house. she needs to enclose the garden with a fence, and will use the house as one side of the fence. If laura has 63 feet of fencing to use, what is the maximum area that she can enclose? What are the dimensions of the garden? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #491857 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=491857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = a dimension and y = the other dimension.\r<BR>\n" );
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document.write( "A is for area.<BR>\n" );
document.write( "A=xy and 2x+y=63; this second equation is for the fencing length.<BR>\n" );
document.write( "You want the maximum A and this you might guess if you look at the two equations, would be a quadratic function.  You can see I am using y as the length of the enclosure which is against the house.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B63 ALIGN=MIDDLE  ALT=\"y=-2x%2B63\"   DISABLED_style= \"max-width:90%; height:auto;\" > is from the fencing length equation;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=x%2A%28-2x%2B63%29 ALIGN=MIDDLE  ALT=\"A=x%2A%28-2x%2B63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-2x%5E2%2B63x ALIGN=MIDDLE  ALT=\"A=-2x%5E2%2B63x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "!.................That function is a parabola, opening downward, so it has a maximum point.  You can find the roots (the values of x for which A is zero) and the x value in the exact middle of those roots will occur at the maximum point of A.\r<BR>\n" );
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document.write( "Here we go:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=0=-2x%5E2%2B63x ALIGN=MIDDLE  ALT=\"A=0=-2x%5E2%2B63x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%28-2x%2B63%29 ALIGN=MIDDLE  ALT=\"0=x%28-2x%2B63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "One possibility for x is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Other possibility for x is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2B63=0 ALIGN=MIDDLE  ALT=\"-2x%2B63=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=63 ALIGN=MIDDLE  ALT=\"2x=63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=63%2F2 ALIGN=MIDDLE  ALT=\"x=63%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x=31%261%2F2=63%2F2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x=31%261%2F2=63%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "'<BR>\n" );
document.write( "The x value in the middle:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2863%2F2%29%2F2=highlight%2863%2F4=15%263%2F4%29 ALIGN=MIDDLE  ALT=\"%2863%2F2%29%2F2=highlight%2863%2F4=15%263%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Going back to the formula for y derived from the fence length above, you should find that y and x are the same value; so the maximum area is a square. </SPAN>\n" );
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