document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=895796>Question 895796</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 64. Show that their product has a maximum of 1024. Many thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543013 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=543013\">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=x%2By=64 ALIGN=MIDDLE  ALT=\"x%2By=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%3C=1024 ALIGN=MIDDLE  ALT=\"xy%3C=1024\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=64-x ALIGN=MIDDLE  ALT=\"y=64-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2864-x%29=f ALIGN=MIDDLE  ALT=\"x%2864-x%29=f\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----the product of x and y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=64x-x%5E2 ALIGN=MIDDLE  ALT=\"f=64x-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=-x%5E2%2B64x ALIGN=MIDDLE  ALT=\"f=-x%5E2%2B64x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Complete The Square.    Use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2864%2F2%29%5E2=32%5E2 ALIGN=MIDDLE  ALT=\"%2864%2F2%29%5E2=32%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=-1%28x%5E2-64x%29 ALIGN=MIDDLE  ALT=\"f=-1%28x%5E2-64x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=-1%28x%5E2-64x%2B32%5E2-32%5E2%29 ALIGN=MIDDLE  ALT=\"f=-1%28x%5E2-64x%2B32%5E2-32%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=-1%28%28x-32%29%5E2-32%5E2%29 ALIGN=MIDDLE  ALT=\"f=-1%28%28x-32%29%5E2-32%5E2%29\"   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%28f=-%28x-32%29%5E2%2B32%5E2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28f=-%28x-32%29%5E2%2B32%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ standard form, parabolic function.\r<BR>\n" );
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document.write( "The maximum, the vertex of f is at (32,32^2) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%5E2=1024 ALIGN=MIDDLE  ALT=\"32%5E2=1024\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "(See my lesson on Completing The Square)<BR>\n" );
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