document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=530268>Question 530268</A>: <I><SPAN STYLE=\"word-break: break-all;\"> parabola,x^2 +6x -y +11 =0<BR>\n" );
document.write( "find the vertex,focus and directrix of the parabola </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350038 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=350038\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> parabola,x^2 +6x -y +11 =0<BR>\n" );
document.write( "find the vertex,focus and directrix of the parabola<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Standard form of equation for parabola: (x-h)^2=4p(y-k), (h,k) being the (x,y) coordinates of the vertex.<BR>\n" );
document.write( "x^2 +6x -y +11 =0<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "y=(x^2+6x+9)+11-9<BR>\n" );
document.write( "y=(x+3)^2+2<BR>\n" );
document.write( "Rewrite in standard form<BR>\n" );
document.write( "(x+3)^2=(y-2)<BR>\n" );
document.write( "Vertex: (-3,2)<BR>\n" );
document.write( "4p=1<BR>\n" );
document.write( "p=1/4<BR>\n" );
document.write( "focus: (-3,9/4)<BR>\n" );
document.write( "directrix: y=7/4 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );