document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133489>Question 133489</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/157232184921479/algebrahomeworkh>frogs, fleas, and painted cubes</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I'm having promblems understanding how to find the info i need to graph this equation.....\r<BR>\n" );
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document.write( "I could possibly have the wrong equation.\r<BR>\n" );
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document.write( "L x 15 -L ( this is the eqution I came up with)\r<BR>\n" );
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document.write( "the original equation is .... The rectangle has a perimeter of 30 meters and a side length of l,       A=?\r<BR>\n" );
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document.write( "Thank you for your help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97675 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=97675\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So far, so good.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2A%2815-L%29 ALIGN=MIDDLE  ALT=\"A=L%2A%2815-L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is absolutely correct.  But you probably want to put this into standard form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-L%5E2%2B15L ALIGN=MIDDLE  ALT=\"A=-L%5E2%2B15L\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is just a quadratic in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, substituting L for the independent variable x and with coefficients as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=15 ALIGN=MIDDLE  ALT=\"b=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=0 ALIGN=MIDDLE  ALT=\"c=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The vertex of the parabola has an x-coordinate at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a ALIGN=MIDDLE  ALT=\"-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15%2F2%28-1%29=15%2F2 ALIGN=MIDDLE  ALT=\"-15%2F2%28-1%29=15%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The y-coordinate of the vertex is equal to the value of the function at the x-coordinate, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2815%2F4%29%5E2%2B15%2815%2F2%29=-225%2F4%2B225%2F2=225%2F4 ALIGN=MIDDLE  ALT=\"-%2815%2F4%29%5E2%2B15%2815%2F2%29=-225%2F4%2B225%2F2=225%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence the vertex of the graph is at (15/2,225/4).\r<BR>\n" );
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document.write( "Factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-L%5E2%2B15L ALIGN=MIDDLE  ALT=\"-L%5E2%2B15L\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2815-L%29 ALIGN=MIDDLE  ALT=\"L%2815-L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so zeroes of the polynomial are 0 and 15, meaning the x-intercepts are at (0,0) and (15,0).\r<BR>\n" );
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document.write( "Pick a couple other values for L:\r<BR>\n" );
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document.write( "If L = 1, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-%281%29%5E2%2B15%281%29=14 ALIGN=MIDDLE  ALT=\"A=-%281%29%5E2%2B15%281%29=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and by symmetry, if L = 14, A = 14\r<BR>\n" );
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document.write( "If L = 2, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-%282%29%5E2%2B15%282%29=26 ALIGN=MIDDLE  ALT=\"A=-%282%29%5E2%2B15%282%29=26\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and by symmetry, if L = 13, A = 26\r<BR>\n" );
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document.write( "Just plot the points and sketch a smooth curve.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-5%2C20%2C-5%2C60%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28600%2C600%2C-5%2C20%2C-5%2C60%2C-x%5E2%2B15x%29%2C%0D%0Acircle%2815%2F2%2C225%2F4%2C.2%29%2C%0D%0Acircle%280%2C0%2C.2%29%2C%0D%0Acircle%2815%2C0%2C.2%29%2C%0D%0Acircle%281%2C14%2C.2%29%2C%0D%0Acircle%2814%2C14%2C.2%29%2C%0D%0Acircle%282%2C26%2C.2%29%2C%0D%0Acircle%2813%2C26%2C.2%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Super-Double-Plus Extra Credit.  Just looking at this picture, what specific quadrilateral gives the maximum area for a given perimeter? </SPAN>\n" );
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