document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253390>Question 253390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do the graphs of f(x)=x^2 + x and g(x)= x^2+|x| compare?<BR>\n" );
document.write( "A. f(x)=g(x) for x<0<BR>\n" );
document.write( "B. f(x)>g(x) for x<0<BR>\n" );
document.write( "C. f(x)=g(x) for x> or equal to 0<BR>\n" );
document.write( "D. f(x)> g(x) for x> or equal to 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #185739 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=185739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would say selection c.\r<BR>\n" );
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document.write( "when x < 0, f(x) < g(x) so selection a is false.<BR>\n" );
document.write( "when x < 0, f(x) < g(x) so selection b is false.<BR>\n" );
document.write( "when x >= 0 f(x) = g(x) so selection c looks good since |x| = x when x >= 0<BR>\n" );
document.write( "when x >= 0 f(x) = g(x) so selection d is false.\r<BR>\n" );
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document.write( "graph of both equations looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28600%2C600%2C-10%2C10%2C-10%2C200%2Cx%5E2+%2B+x%2Cx%5E2+%2B+abs%28x%29%2C56%2C72%29 ALIGN=MIDDLE  ALT=\"graph+%28600%2C600%2C-10%2C10%2C-10%2C200%2Cx%5E2+%2B+x%2Cx%5E2+%2B+abs%28x%29%2C56%2C72%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can see that when x >= 0 it looks like one graph.\r<BR>\n" );
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document.write( "this is because the 2 equations are identical and become superimposed on each other.\r<BR>\n" );
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document.write( "when x is negative, the graphs are separate.\r<BR>\n" );
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document.write( "the red graph (the lower one) is the equation f(x) = x^2 + x.   \r<BR>\n" );
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document.write( "the green graph (the higher one) is the equation f(x) = x^2 + |x|\r<BR>\n" );
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document.write( "as an example:\r<BR>\n" );
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document.write( "when x = -8, x^2 + x becomes 64 - 8 = 56\r<BR>\n" );
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document.write( "when x = -8 x^2 + |x| becomes 64 + 8 = 72\r<BR>\n" );
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document.write( "I drew horizontal lines at y = 56 and y = 72 so you could see that easier.\r<BR>\n" );
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document.write( "find x = -8 and trace vertically up until you see the intersection points.\r<BR>\n" );
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