document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999340>Question 999340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, <BR>\n" );
document.write( " I need help with this question, it says: Find the discriminant of sqrt((-12)^2 - 4 * 9 * 3), identify the number of the solutions and their types. Graph the possible quadratic function.<BR>\n" );
document.write( "I ended up with +6 and -6 but I have no idea where to go from there or how to graph it. Do I plug in -b and complete the quadratic function or what??<BR>\n" );
document.write( "Help me please! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617016 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=617016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "the discriminant of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-12%29%5E2+-+4+%2A+9+%2A+3%29=sqrt%28144+-+108%29=sqrt%2836%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-12%29%5E2+-+4+%2A+9+%2A+3%29=sqrt%28144+-+108%29=sqrt%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the discriminant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%3E0 ALIGN=MIDDLE  ALT=\"36%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >;  that means quadratic function has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=two ALIGN=MIDDLE  ALT=\"two\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=real ALIGN=MIDDLE  ALT=\"real\"   DISABLED_style= \"max-width:90%; height:auto;\" > solutions \r<BR>\n" );
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document.write( "now, we can find what is the equation:\r<BR>\n" );
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document.write( "recall: the discriminant is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4+%2A+a%2A+c ALIGN=MIDDLE  ALT=\"b%5E2+-+4+%2A+a%2A+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when you compare it to given above,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%5E2+-+4+%2A+9+%2A+3%29 ALIGN=MIDDLE  ALT=\"%28-12%29%5E2+-+4+%2A+9+%2A+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=+-12 ALIGN=MIDDLE  ALT=\"b=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=9 ALIGN=MIDDLE  ALT=\"a=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3 ALIGN=MIDDLE  ALT=\"c=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the possible quadratic function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9x%5E2-12x%2B3 ALIGN=MIDDLE  ALT=\"y=9x%5E2-12x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=two ALIGN=MIDDLE  ALT=\"two\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=real ALIGN=MIDDLE  ALT=\"real\"   DISABLED_style= \"max-width:90%; height:auto;\" > solutions\r<BR>\n" );
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document.write( "let's find them:<BR>\n" );
document.write( "make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=9x%5E2-12x%2B3 ALIGN=MIDDLE  ALT=\"0=9x%5E2-12x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >...both sides divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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=0=3x%5E2-4x%2B1 ALIGN=MIDDLE  ALT=\"0=3x%5E2-4x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >....factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=3x%5E2-3x-x%2B1 ALIGN=MIDDLE  ALT=\"0=3x%5E2-3x-x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >...group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%283x%5E2-3x%29-%28x-1%29 ALIGN=MIDDLE  ALT=\"0=%283x%5E2-3x%29-%28x-1%29\"   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=0=3x%28x-1%29-%28x-1%29 ALIGN=MIDDLE  ALT=\"0=3x%28x-1%29-%28x-1%29\"   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=0=%283x-1%29%28x-1%29 ALIGN=MIDDLE  ALT=\"0=%283x-1%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%283x-1%29 ALIGN=MIDDLE  ALT=\"0=%283x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=1 ALIGN=MIDDLE  ALT=\"3x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=1%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=1%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28x-1%29 ALIGN=MIDDLE  ALT=\"0=%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "see it on the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+10%2C+9x%5E2-12x%2B3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+10%2C+9x%5E2-12x%2B3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );