document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=36047>Question 36047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertex and focus of y=x^2+6x+7 and sketch it's graph. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22068 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=22068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the vertex and focus of y=x^2+6x+7 and sketch it's graph.<BR>\n" );
document.write( "Y=X^2+2*X*3+3^2-3^2+7=(X+3)^2-2<BR>\n" );
document.write( "Y+2=1(X+3)^2<BR>\n" );
document.write( "COMPARING WITH STD.EQN.OF PARABOLA<BR>\n" );
document.write( "(X-H)^2=4A(Y-K)..WHOSE VERTEX IS (H,K)AND FOCUS IS (H,K+A)<BR>\n" );
document.write( "(X+3)^2=(Y+2)<BR>\n" );
document.write( "WE FIND H=-3...K=-2......A=1/4.......HENCE<BR>\n" );
document.write( "VERTEX IS (-3,-2) AND <BR>\n" );
document.write( "FOCUS IS (-3,-2+1/4)=(-3,-7/4)<BR>\n" );
document.write( "GRAPH IS<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+5%2C+-10%2C+50%2C+x%5E2%2B6x%2B7%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+5%2C+-10%2C+50%2C+x%5E2%2B6x%2B7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );