document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1057566>Question 1057566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial function whose graph passes through (-1,-11),(0,-6),(1,-3), and (2,4). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #672724 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=672724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use a general cubic equation since you have 4 points.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E3%2Bbx%5E2%2Bcx%2Bd ALIGN=MIDDLE  ALT=\"y=ax%5E3%2Bbx%5E2%2Bcx%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(-1,-11)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11=a%28-1%29%5E3%2Bb%28-1%29%5E2%2Bc%28-1%29%2Bd ALIGN=MIDDLE  ALT=\"-11=a%28-1%29%5E3%2Bb%28-1%29%5E2%2Bc%28-1%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Bb-c%2Bd=-11 ALIGN=MIDDLE  ALT=\"-a%2Bb-c%2Bd=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(0,-6)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6=a%280%29%5E3%2Bb%280%29%5E2%2Bc%280%29%2Bd ALIGN=MIDDLE  ALT=\"-6=a%280%29%5E3%2Bb%280%29%5E2%2Bc%280%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-6 ALIGN=MIDDLE  ALT=\"d=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1,-3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3=a%281%29%5E3%2Bb%281%29%5E2%2Bc%281%29%2Bd ALIGN=MIDDLE  ALT=\"-3=a%281%29%5E3%2Bb%281%29%5E2%2Bc%281%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc%2Bd=-3 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc%2Bd=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2,4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=a%282%29%5E3%2Bb%282%29%5E2%2Bc%282%29%2Bd ALIGN=MIDDLE  ALT=\"4=a%282%29%5E3%2Bb%282%29%5E2%2Bc%282%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8a%2B4b%2B2c%2Bd=4 ALIGN=MIDDLE  ALT=\"8a%2B4b%2B2c%2Bd=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the result from 2 on the 3 other equations,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Bb-c-6=-11 ALIGN=MIDDLE  ALT=\"-a%2Bb-c-6=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Bb-c=-5 ALIGN=MIDDLE  ALT=\"-a%2Bb-c=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc-6=-3 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc-6=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "6.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=3 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8a%2B4b%2B2c-6=4 ALIGN=MIDDLE  ALT=\"8a%2B4b%2B2c-6=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8a%2B4b%2B2c=10 ALIGN=MIDDLE  ALT=\"8a%2B4b%2B2c=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "7.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b%2Bc=5 ALIGN=MIDDLE  ALT=\"4a%2B2b%2Bc=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 5 to 7 and subtract 6 from 7 to get two new equations eliminating c.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b%2Bc-a%2Bb-c=5-5 ALIGN=MIDDLE  ALT=\"4a%2B2b%2Bc-a%2Bb-c=5-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2B3b=0 ALIGN=MIDDLE  ALT=\"3a%2B3b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "8.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=0 ALIGN=MIDDLE  ALT=\"a%2Bb=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b%2Bc-a-b-c=5-3 ALIGN=MIDDLE  ALT=\"4a%2B2b%2Bc-a-b-c=5-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "9.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2Bb=2 ALIGN=MIDDLE  ALT=\"3a%2Bb=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 8 from 9 to eliminate b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2Bb-a-b=2-0 ALIGN=MIDDLE  ALT=\"3a%2Bb-a-b=2-0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a=2 ALIGN=MIDDLE  ALT=\"2a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\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;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bb=0 ALIGN=MIDDLE  ALT=\"1%2Bb=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1%2Bc=3 ALIGN=MIDDLE  ALT=\"1-1%2Bc=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E3-x%5E2%2B3x-6 ALIGN=MIDDLE  ALT=\"y=x%5E3-x%5E2%2B3x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );