document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=710263>Question 710263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what are the vertex, focus and directrix of parabola  12y=x^2-6x+45?  have so far:  (x-3)^2=12(y-3).  vertex is (3,3) or (-3,-3)????  how do I do focus and directrix? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436991 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=436991\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what are the vertex, focus and directrix of parabola <BR>\n" );
document.write( "12y=x^2-6x+45?<BR>\n" );
document.write( "x^2-6x=12y-45<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "(x^2-6x+9)=12y-45+9<BR>\n" );
document.write( "(x-3)^2=12y-36<BR>\n" );
document.write( "(x-3)^2=12(y-3)<BR>\n" );
document.write( "This is an equation of a parabola that opens upwards.<BR>\n" );
document.write( "Its standard form: (x-h)^2=4p(y-k), (h,k)=(x,y) coordinates of the vertex<BR>\n" );
document.write( "For given equation:(x-3)^2=12(y-3)<BR>\n" );
document.write( "vertex: (3,3)<BR>\n" );
document.write( "axis of symmetry: x=3<BR>\n" );
document.write( "4p=12<BR>\n" );
document.write( "p=3<BR>\n" );
document.write( "focus: (3,6) (p-units above vertex on the axis of symmetry)<BR>\n" );
document.write( "directrix: y=0 (p-units below vertex on the axis of symmetry) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );