document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=783360>Question 783360</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the vertex, focus and directrix of the following:<BR>\n" );
document.write( "4y^2+4x+4y-3=0<BR>\n" );
document.write( "2x^2-12X+3y+21=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #476819 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=476819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the vertex, focus and directrix of the following:<BR>\n" );
document.write( "4y^2+4x+4y-3=0<BR>\n" );
document.write( "4y^2+4y+4x-3=0<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "4(y^2+y+1/4)-1+4x-3=0<BR>\n" );
document.write( "4(y+1/2)^2=-4x+4<BR>\n" );
document.write( "4(y+1/2)^2=-4(x-1)<BR>\n" );
document.write( "divide by 4<BR>\n" );
document.write( "(y+1/2)^2=-(x-1)<BR>\n" );
document.write( "This is a parabola that opens leftward.<BR>\n" );
document.write( "Its basic form of equation: (y+k)^2=-4p(x-h), (h,k)=(x,y) coordinates of the vertex<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "vertex: (1,-1/2)<BR>\n" );
document.write( "axis of symmetry: y=-1/2<BR>\n" );
document.write( "4p=1<BR>\n" );
document.write( "p=1/4<BR>\n" );
document.write( "focus: (3/4,-1/2) (p-distance left of vertex on the axis of symmetry<BR>\n" );
document.write( "directrix: x=5/4 (p-distance right of vertex on the axis of symmetry<BR>\n" );
document.write( "..<BR>\n" );
document.write( "2x^2-12x+3y+21=0<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "2(x^2-6x+9)-18+3y+21=0<BR>\n" );
document.write( "2(x-3)^2=-3y+3<BR>\n" );
document.write( "2(x-3)^2=-3(y+1)<BR>\n" );
document.write( "(x-3)^2=-3/2(y+1)<BR>\n" );
document.write( "This is a parabola that opens downward.<BR>\n" );
document.write( "Its basic form of equation: (x-h)^2=-4p(y-k), (h,k)=(x,y) coordinates of the vertex<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "vertex: (3,-1)<BR>\n" );
document.write( "axis of symmetry: x=3<BR>\n" );
document.write( "4p=3/2<BR>\n" );
document.write( "p=3/8<BR>\n" );
document.write( "focus: (3,-11/8) (p-distance below vertex on the axis of symmetry<BR>\n" );
document.write( "directrix: y=-5/8 (p-distance above vertex on the axis of symmetry<BR>\n" );
document.write( ".. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );