document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=545587>Question 545587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> put in standard form and graph x^2-2x+y+7<BR>\n" );
document.write( "find the 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 #357025 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=357025\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> put in standard form and graph x^2-2x+y+7<BR>\n" );
document.write( "find the focus and directrix<BR>\n" );
document.write( "**<BR>\n" );
document.write( "x^2-2x+y+7=0<BR>\n" );
document.write( "y=-x^2+2x-7<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "y=-(x^2-2x+1)-7+1<BR>\n" );
document.write( "y=-(x-1)^2-6<BR>\n" );
document.write( "(x-1)^2=-(y+6)<BR>\n" );
document.write( "This equation is in standard form for a parabola: (x-h)^2=4p(y-k), with (h,k) being the (x,y) coordinates of the vertex. Parabola opens downwards.<BR>\n" );
document.write( "For given equation:(x-1)^2=-(y+6)<BR>\n" );
document.write( "vertex: (1,-6)<BR>\n" );
document.write( "axis of symmetry: x=1<BR>\n" );
document.write( "4p=1<BR>\n" );
document.write( "p=1/4<BR>\n" );
document.write( "Focus and directrix are p units from the vertex on the axis of symmetry<BR>\n" );
document.write( "Focus: (1, -6+p)=(1,-6-1/4)=1,-25/4)<BR>\n" );
document.write( "Directrix: y=-6+1/4=-23/4 </SPAN>\n" );
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