document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144838>Question 144838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Apply the quadratic formula to find the roots of the given function, and then graph the function.\r<BR>\n" );
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document.write( "g(x) = x2 + x + 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105526 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=105526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%2B12=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=12 ALIGN=MIDDLE  ALT=\"c=12\"   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=x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A12+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A12+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=1, and c=12\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A12+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A12+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 1 to get 1  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+sqrt%28+1%2B-48+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%2B-48+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A12%2A1 ALIGN=MIDDLE  ALT=\"-4%2A12%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48 ALIGN=MIDDLE  ALT=\"-48\"   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=x+=+%28-1+%2B-+sqrt%28+-47+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+-47+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+i%2Asqrt%2847%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+i%2Asqrt%2847%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+i%2Asqrt%2847%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+i%2Asqrt%2847%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\r<BR>\n" );
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document.write( "So the roots are\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B+i%2Asqrt%2847%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B+i%2Asqrt%2847%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+-+i%2Asqrt%2847%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-1+-+i%2Asqrt%2847%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice if we graph the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2Bx%2B12 ALIGN=MIDDLE  ALT=\"y=x%5E2%2Bx%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we 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+-15.5%2C+14.5%2C+-3.25%2C+26.75%2C+x%5E2%2Bx%2B12%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-15.5%2C+14.5%2C+-3.25%2C+26.75%2C+x%5E2%2Bx%2B12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2Bx%2B12 ALIGN=MIDDLE  ALT=\"y=x%5E2%2Bx%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can see that there are no real roots<BR>\n" );
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