document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28016>Question 28016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the equation of a parabola that passes through the points (1,6),(-2,27), (2,11)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15259 by </B><A HREF=/tutors/aboutme.mpl?userid=bmauger><B>bmauger(101)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bmauger><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=15259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A quadratic equation can be written in the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > By putting in the three points given we can get three linear equations of the three variables a, b, & c and then solve:<BR>\n" );
document.write( "evaluating <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > for (1,6) we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=a%281%29%5E2%2Bb%281%29%2Bc ALIGN=MIDDLE  ALT=\"6=a%281%29%5E2%2Bb%281%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "Eq 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=a%2Bb%2Bc ALIGN=MIDDLE  ALT=\"6=a%2Bb%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "For (-2, 27)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27=a%28-2%29%5E2%2Bb%28-2%29%2Bc ALIGN=MIDDLE  ALT=\"27=a%28-2%29%5E2%2Bb%28-2%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Eq 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27=4a-2b%2Bc ALIGN=MIDDLE  ALT=\"27=4a-2b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "For (2, 11)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11=a%282%29%5E2%2Bb%282%29%2Bc ALIGN=MIDDLE  ALT=\"11=a%282%29%5E2%2Bb%282%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Eq 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11=4a%2B2b%2Bc ALIGN=MIDDLE  ALT=\"11=4a%2B2b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now you simply solve the three simolutanious equations for a, b, and c.<BR>\n" );
document.write( "To get you started, let's subtract equation 1 from equation 3 to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11=4a%2B2b%2Bc ALIGN=MIDDLE  ALT=\"11=4a%2B2b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=a%2Bb%2Bc ALIGN=MIDDLE  ALT=\"6=a%2Bb%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=3a%2Bb ALIGN=MIDDLE  ALT=\"5=3a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then subtract equation 1 from equation 2 to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27=4a-2b%2Bc ALIGN=MIDDLE  ALT=\"27=4a-2b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=a%2Bb%2Bc ALIGN=MIDDLE  ALT=\"6=a%2Bb%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21=3a-3b ALIGN=MIDDLE  ALT=\"21=3a-3b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the two new equations we found should be enough to get you to the answer in a few more steps. When you get there put your a, b, and c in for: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that's your answer (unless you're supposed to factor or find the roots, graph it, or do anything else to the equation). </SPAN>\n" );
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