document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=289111>Question 289111</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph f(x)<= x^2-x-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209472 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=209472\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simply graph the polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-1 ALIGN=MIDDLE  ALT=\"x%5E2-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-x-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-x-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now just shade the ENTIRE region below the curve. This shaded region is the red region shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+y%3C=x%5E2-x-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+y%3C=x%5E2-x-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So why did we shade below? Since f(x) is really 'y' and f(x) is less than or equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-1 ALIGN=MIDDLE  ALT=\"x%5E2-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that all of the y values that satisfy <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3Cx%5E2-x-1 ALIGN=MIDDLE  ALT=\"y%3Cx%5E2-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be below the curve.\r<BR>\n" );
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