document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119534>Question 1119534</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch the curve, find the coordinate of the vertex and focus, and find the equation of the axis and directrix of x^2 - 6x + 8y + 25 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735131 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=735131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The equation has an x^2 term; the parabola opens either up or down.  The general form of the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-k+=+%281%2F%284p%29%29%28x-h%29%5E2 ALIGN=MIDDLE  ALT=\"y-k+=+%281%2F%284p%29%29%28x-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "where (h,k) is the vertex and p is the directed distance from the directrix to the vertex and from the vertex to the focus.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B8y%2B25+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B8y%2B25+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x+=+-8y-25 ALIGN=MIDDLE  ALT=\"x%5E2-6x+=+-8y-25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9+=+-8y-25%2B9+=+-8y-16 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9+=+-8y-25%2B9+=+-8y-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+=+-8%28y%2B2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+=+-8%28y%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2+=+%28-1%2F8%29%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"y%2B2+=+%28-1%2F8%29%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28-2%29+=+%281%2F%284%28-2%29%29%29%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"y-%28-2%29+=+%281%2F%284%28-2%29%29%29%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "This is in the required form.  The vertex is (3,-2); p = -2.<br><BR>\n" );
document.write( "With vertex (3,-2) and p=-2, the focus is at (3,-4); the directrix is y=0; and the axis is x=3.<br><BR>\n" );
document.write( "A graph...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C10%2C-10%2C5%2C%28-1%2F8%29%28x-3%29%5E2-2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C10%2C-10%2C5%2C%28-1%2F8%29%28x-3%29%5E2-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );