document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=857853>Question 857853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertex, focus, and directrix of th eparabola given by the equation<BR>\n" );
document.write( "x^2 - 8x -16y + 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516991 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=516991\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Something is missing. An <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28equa%29 ALIGN=MIDDLE  ALT=\"red%28equa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tion ALIGN=MIDDLE  ALT=\"tion\"   DISABLED_style= \"max-width:90%; height:auto;\" > must have an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28equa%29 ALIGN=MIDDLE  ALT=\"red%28equa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l ALIGN=MIDDLE  ALT=\"l\"   DISABLED_style= \"max-width:90%; height:auto;\" > sign.<BR>\n" );
document.write( "Maybe you meant to type <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+8x+-16y=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+8x+-16y=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you got a + sign instead of the = sign.<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x-16y=0 ALIGN=MIDDLE  ALT=\"x%5E2-8x-16y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x=16y ALIGN=MIDDLE  ALT=\"x%5E2-8x=16y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B16=16y%2B16 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B16=16y%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2=16%28y%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2=16%28y%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B1=%281%2F16%29%28x-4%29%5E2 ALIGN=MIDDLE  ALT=\"y%2B1=%281%2F16%29%28x-4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F16%29%28x-4%29%5E2%7D-1 ALIGN=MIDDLE  ALT=\"y=%281%2F16%29%28x-4%29%5E2%7D-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is the equation of a parabola with the vertical axis of symmetry<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=0 ALIGN=MIDDLE  ALT=\"x-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the vertex at (4,-1), which is the lowest value <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > can take,<BR>\n" );
document.write( "and a focal distance of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F4=4 ALIGN=MIDDLE  ALT=\"16%2F4=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That means that the focus is (4,3),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > units above the vertex,<BR>\n" );
document.write( "and the directrix is the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5 ALIGN=MIDDLE  ALT=\"y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > units below the vertex.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-6%2C14%2C-6%2C14%2C%0D%0Agraph%28300%2C300%2C-6%2C14%2C-6%2C14%2C%28x-4%29%5E2%2F16-1%2C-5%29%2C%0D%0Agreen%28circle%284%2C-1%2C0.2%29%29%2Cgreen%28circle%284%2C3%2C0.2%29%29%2C%0D%0Ablue%28circle%2812%2C3%2C0.2%29%29%2Cblue%28arrow%287.5%2C3%2C4.2%2C3%29%29%2C%0D%0Ablue%28arrow%288.5%2C3%2C11.8%2C3%29%29%2Cblue%28arrow%2812%2C-1.05%2C12%2C2.8%29%29%2C%0D%0Ablue%28arrow%2812%2C-2.1%2C12%2C-5%29%29%2Clocate%2811.7%2C-1.1%2C8%29%2C%0D%0Alocate%287.8%2C3.5%2C8%29%2Clocate%284.1%2C1.4%2C4%29%2Clocate%284.1%2C-2.6%2C4%29%2C%0D%0Aarrow%284%2C-5%2C4%2C-1.2%29%2Carrow%284%2C-1.2%2C4%2C-5%29%2C%0D%0Aarrow%284%2C2.8%2C4%2C-0.8%29%2Carrow%284%2C-0.8%2C4%2C2.8%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );