document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=530608>Question 530608</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the vertex,focus,axis and directrix of the equation <BR>\n" );
document.write( "y^2-4y-4x-8=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350610 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=350610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the vertex,focus,axis and directrix of the equation <BR>\n" );
document.write( "y^2-4y-4x-8=0<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "(y^2-4y+4)=4x+8+4<BR>\n" );
document.write( "(y-2)^2=4x+12<BR>\n" );
document.write( "(y-2)^2=4(x+3)<BR>\n" );
document.write( "This is an equation of a parabola of the standard form: (y-k)^2=4p(x-h), (h,k) being the (x,y) coordinates of the vertex. Parabola opens rightwards.<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "vertex: (-3,2)<BR>\n" );
document.write( "4p=4<BR>\n" );
document.write( "p=1<BR>\n" );
document.write( "Focus=(-3+p,2)=(-3+1,2)=(-2,2) (p units from vertex on axis of symmetry)<BR>\n" );
document.write( "Axis of symmetry: y=2 (a horizontal line thru the vertex)<BR>\n" );
document.write( "Directrix: x=-4 (a vertical line p units from vertex on axis of symmetry) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );