document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90408>Question 90408</A>: <I><SPAN STYLE=\"word-break: break-all;\">  5a) Calculate the value of the discriminant of  x^2+4x+4=0\r<BR>\n" );
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document.write( "B)  By examining the sign of the discriminant in part a, how many x-intercepts  would the graph of y=x^2+4x+4 have? Why?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65604 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=65604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Discriminant:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=b%5E2-4ac ALIGN=MIDDLE  ALT=\"D=b%5E2-4ac\"   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=D=4%5E2-4%281%29%284%29 ALIGN=MIDDLE  ALT=\"D=4%5E2-4%281%29%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=4, a=4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=16-4%281%29%284%29 ALIGN=MIDDLE  ALT=\"D=16-4%281%29%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 4 to get 16 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=16-16%29 ALIGN=MIDDLE  ALT=\"D=16-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A4%2A1 ALIGN=MIDDLE  ALT=\"-4%2A4%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   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=D=0 ALIGN=MIDDLE  ALT=\"D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "So a discriminant of zero means there is only one x-intercept\r<BR>\n" );
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document.write( "When you perform the quadratic formula, you would get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x=\frac{4\pm sqrt{0}}{2}\"> Plug the discriminant into the formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x=\frac{4\pm0}{2}\"> Take the square root\r<BR>\n" );
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document.write( "So the expression breaks up to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x=\frac{4+0}{2}\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x=\frac{4-0}{2}\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x=\frac{4}{2}\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x=\frac{4}{2}\"> Add/subtract 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x=2\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x=2\"> Simplify\r<BR>\n" );
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document.write( "So we can see that the two values are the same answer </SPAN>\n" );
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