document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196172>Question 1196172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A function is defined by g:x=ax²+bx+2 where a and b are constants. If g(-2)=6 and g(3)=11, Find the values of a and b<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828890 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=828890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "A function is defined by:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=ax%5E2%2Bbx%2B2 ALIGN=MIDDLE  ALT=\"g%28x%29=ax%5E2%2Bbx%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b ALIGN=MIDDLE  ALT=\"+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > are constants\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-2%29=6+ ALIGN=MIDDLE  ALT=\"g%28-2%29=6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=a%28-2%29%5E2%2Bb%28-2%29%2B2 ALIGN=MIDDLE  ALT=\"6=a%28-2%29%5E2%2Bb%28-2%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=4a-2b%2B2 ALIGN=MIDDLE  ALT=\"6=4a-2b%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >............solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%2B6-2=4a ALIGN=MIDDLE  ALT=\"2b%2B6-2=4a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%2B4=4a ALIGN=MIDDLE  ALT=\"2b%2B4=4a\"   DISABLED_style= \"max-width:90%; height:auto;\" > ............simplify\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B2=2a+ ALIGN=MIDDLE  ALT=\"b%2B2=2a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=+b%2F2%2B1 ALIGN=MIDDLE  ALT=\"a=+b%2F2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >...............eq.1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%283%29=11 ALIGN=MIDDLE  ALT=\"g%283%29=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11=a%283%29%5E2%2Bb%283%29%2B2 ALIGN=MIDDLE  ALT=\"11=a%283%29%5E2%2Bb%283%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11=9a%2B3b%2B2 ALIGN=MIDDLE  ALT=\"11=9a%2B3b%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11-2-3b=9a+ ALIGN=MIDDLE  ALT=\"11-2-3b=9a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-3b=9a+ ALIGN=MIDDLE  ALT=\"9-3b=9a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=9%2F9-3b%2F9 ALIGN=MIDDLE  ALT=\"a=9%2F9-3b%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1-b%2F3 ALIGN=MIDDLE  ALT=\"a=1-b%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >................eq.2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "from eq.1 and eq.2 we have\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F2%2B1=1-b%2F3 ALIGN=MIDDLE  ALT=\"b%2F2%2B1=1-b%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F2%2Bb%2F3=1-1 ALIGN=MIDDLE  ALT=\"b%2F2%2Bb%2F3=1-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F2%2Bb%2F3=0 ALIGN=MIDDLE  ALT=\"b%2F2%2Bb%2F3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> will be true <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=only ALIGN=MIDDLE  ALT=\"only\"   DISABLED_style= \"max-width:90%; height:auto;\" > if<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=0 ALIGN=MIDDLE  ALT=\"+b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "go to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1-b%2F3 ALIGN=MIDDLE  ALT=\"a=1-b%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >................eq.2, plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we get \r<BR>\n" );
document.write( "\n" );
document.write( "<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;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+ ALIGN=MIDDLE  ALT=\"a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+ ALIGN=MIDDLE  ALT=\"1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+ ALIGN=MIDDLE  ALT=\"0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >respectively\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and your function is: \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=1%2Ax%5E2%2B0%2Ax%2B2+ ALIGN=MIDDLE  ALT=\"g%28x%29=1%2Ax%5E2%2B0%2Ax%2B2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=x%5E2%2B2+ ALIGN=MIDDLE  ALT=\"g%28x%29=x%5E2%2B2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );