document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=596993>Question 596993</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertex,focus,and directrix of the equation; x^2+4x+6y-2=0\r<BR>\n" );
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document.write( "(What I've tried)<BR>\n" );
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document.write( " X^2+4x+6y-2=0\r<BR>\n" );
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document.write( " (x+2)^2 = 6y+2 (here's where i'm confusing myself)<BR>\n" );
document.write( " (x+2)^2 = 6(y+2)? If that's right then it should be...<BR>\n" );
document.write( " (x+2)^2 = 4(6/4)(y+2)  <BR>\n" );
document.write( " P=(6/4)<BR>\n" );
document.write( " Vertex = (-2,-2)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378012 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=378012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the vertex,focus,and directrix of the equation; <BR>\n" );
document.write( "x^2+4x+6y-2=0<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "(x^2+4x+4)+6y-2-4=0<BR>\n" );
document.write( "(x+2)^2=-6y+6<BR>\n" );
document.write( "(x+2)^2=-6(y-1)<BR>\n" );
document.write( "This is an equation of a parabola that opens downwards of the standard form:<BR>\n" );
document.write( "(x-h)^2=-4p(y-k), (h,k)=(x,y) coordinates of vertex<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "vertex:(-2,1)<BR>\n" );
document.write( "axis of symmetry: x=-2<BR>\n" );
document.write( "4p=6<BR>\n" );
document.write( "p=3/2<BR>\n" );
document.write( "focus:(-2,1-3/2)=(-2,1/2) (p units below vertex on axis of symmetry)<BR>\n" );
document.write( "directrix: y=1+3/2<BR>\n" );
document.write( "directrix: y=5/2 (p units above vertex on axis of symmetry)\r<BR>\n" );
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