document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=618495>Question 618495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the vertex, focus, directrix, and axis of symmetry of the parabola?\r<BR>\n" );
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document.write( "x^2-2x+8y+9=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388951 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=388951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do you find the vertex, focus, directrix, and axis of symmetry of the parabola? <BR>\n" );
document.write( "x^2-2x+8y+9=0<BR>\n" );
document.write( "complete he square<BR>\n" );
document.write( "(x^2-2x+1)+8y+9-1=0<BR>\n" );
document.write( "(x-1)^2=-8y-8<BR>\n" );
document.write( "(x-1)^2=-8(y+1)<BR>\n" );
document.write( "This is an equation of a parabola that opens downwards<BR>\n" );
document.write( "Form of equation: (x-h)^2=-4p(y-k), (h,k)=(x,y) coordinates of vertex<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "vertex:(1,-1)<BR>\n" );
document.write( "axis of symmetry: x=1<BR>\n" );
document.write( "4p=8<BR>\n" );
document.write( "p=2<BR>\n" );
document.write( "focus: (1,-1-p)=(1,-1-2)=(1,-3) (p units below vertex on axis of symmetry)<BR>\n" );
document.write( "directrix: y=-1+p=-1+2=1 (p units above vertex on axis of symmetry) </SPAN>\n" );
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