document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=710011>Question 710011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch a graph of the equation.<BR>\n" );
document.write( "x=3y^2-18y+23\r<BR>\n" );
document.write( "\n" );
document.write( "Please explain and help me! I know you have to complete the square. I tried, but then some parts made me confused. Thank you for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436830 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=436830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That would be a parabola opening to the right and vertex to the left.  You would want to complete the square for the y terms.  Start by factoring to reverse-distribute the 3 leading coefficient.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x=3y^2-18y+23<BR>\n" );
document.write( "x= 3(y^2-6y ________)+23, and you want to know what term to add and subtract.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The missing square you want is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%286%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or 9.  \r<BR>\n" );
document.write( "\n" );
document.write( "Add the 9 inside the parentheses and you would need to subtract something outside the parentheses.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%28y%5E2-6y%2B9%29%2B23+-+3%2A9 ALIGN=MIDDLE  ALT=\"x=3%28y%5E2-6y%2B9%29%2B23+-+3%2A9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Do you know why we add the 9 inside the parentheses but subtract 3*9 outside of the parentheses?  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "But, to continue,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%28y%5E2-6y%2B9%29%2B23-27 ALIGN=MIDDLE  ALT=\"x=3%28y%5E2-6y%2B9%29%2B23-27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%28y-3%29%5E2-4 ALIGN=MIDDLE  ALT=\"x=3%28y-3%29%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This would be moved upward by 3 units and moved rightward by 4 units.  The vertex is at point (3,-4) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );