document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206103>Question 1206103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation in the form y=ax^2+bx+c for the parabola passing through the points (-1,0),(2,-54),(5,-252) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843332 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843332\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Plug each (x,y) pair into the general form of the equation to get three equations in a, b, and c; then solve that system of equations.<br><BR>\n" );
document.write( "(-1,0): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b%2Bc=0 ALIGN=MIDDLE  ALT=\"a-b%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<br><BR>\n" );
document.write( "(2,-54): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b%2Bc=-54 ALIGN=MIDDLE  ALT=\"4a%2B2b%2Bc=-54\"   DISABLED_style= \"max-width:90%; height:auto;\" > [2]<br><BR>\n" );
document.write( "(5,-252): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25a%2B5b%2Bc=-252 ALIGN=MIDDLE  ALT=\"25a%2B5b%2Bc=-252\"   DISABLED_style= \"max-width:90%; height:auto;\" > [3]<br><BR>\n" );
document.write( "Eliminate c between [1] and [2], and between [2] and [3], to get two equations in a and b.<br><BR>\n" );
document.write( "[2]-[1]: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2B3b=-54 ALIGN=MIDDLE  ALT=\"3a%2B3b=-54\"   DISABLED_style= \"max-width:90%; height:auto;\" > [4]<br><BR>\n" );
document.write( "[3]-[2]: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21a%2B3b=-198 ALIGN=MIDDLE  ALT=\"21a%2B3b=-198\"   DISABLED_style= \"max-width:90%; height:auto;\" > [5]<br><BR>\n" );
document.write( "Eliminate b between [4] and [5] and solve for a.<br><BR>\n" );
document.write( "[5]-[4]: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18a=-144 ALIGN=MIDDLE  ALT=\"18a=-144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-144%2F18=-8 ALIGN=MIDDLE  ALT=\"a=-144%2F18=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substitute a=-8 in [4] and solve for b:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24%2B3b=-54 ALIGN=MIDDLE  ALT=\"-24%2B3b=-54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3b=-30 ALIGN=MIDDLE  ALT=\"3b=-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-10 ALIGN=MIDDLE  ALT=\"b=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substitute a=-8 and b=-10 in [1] and solve for c:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2B10%2Bc=0 ALIGN=MIDDLE  ALT=\"-8%2B10%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-2 ALIGN=MIDDLE  ALT=\"c=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8x%5E2-10x-2 ALIGN=MIDDLE  ALT=\"y=-8x%5E2-10x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Simplified....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%284x%5E2%2B5x%2B1%29 ALIGN=MIDDLE  ALT=\"y=-2%284x%5E2%2B5x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%28x%2B1%29%284x%2B1%29 ALIGN=MIDDLE  ALT=\"y=-2%28x%2B1%29%284x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=%28-2%29%280%29%28-3%29=0 ALIGN=MIDDLE  ALT=\"f%28-1%29=%28-2%29%280%29%28-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=%28-2%29%283%29%289%29=-54 ALIGN=MIDDLE  ALT=\"f%282%29=%28-2%29%283%29%289%29=-54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=%28-2%29%286%29%2821%29=-252 ALIGN=MIDDLE  ALT=\"f%285%29=%28-2%29%286%29%2821%29=-252\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );