document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=617173>Question 617173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the vertex, focus, and dirtectrix of the parabola with the given equation?\r<BR>\n" );
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document.write( "24y = x^2 - 10x + 145 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388191 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=388191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What are the vertex, focus, and dirtectrix of the parabola with the given equation? <BR>\n" );
document.write( "24y = x^2 - 10x + 145<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "24y=(x^2-10x+25)+145-25<BR>\n" );
document.write( "24y=(x-5)^2+120<BR>\n" );
document.write( "(x-5)^2=24y-120<BR>\n" );
document.write( "(x-5)^2=24(y-5)<BR>\n" );
document.write( "This is an equation for 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-5)^2=24(y-5)<BR>\n" );
document.write( "vertex:(5,5)<BR>\n" );
document.write( "4p=24<BR>\n" );
document.write( "p=6<BR>\n" );
document.write( "focus: (5,5+p)<BR>\n" );
document.write( "=(5,5+6)<BR>\n" );
document.write( "=(5,11)<BR>\n" );
document.write( "directrix: y=5-p=5-6=-1<BR>\n" );
document.write( " </SPAN>\n" );
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