document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138077>Question 1138077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertex, focus, directrix, and focal width of the parabola. choices below (5 points) <BR>\n" );
document.write( "negative 1 divided by 16 times x squared = y<BR>\n" );
document.write( "Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "Vertex: (0, 0); Focus: (-8, 0); Directrix: x = 4; Focal width: 64<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "Vertex: (0, 0); Focus: (0, 4); Directrix: y = -4; Focal width: 4<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 64<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755999 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=755999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the vertex, focus, directrix, and focal width of the parabola. choices below  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F+16%29x%5E2+=+y ALIGN=MIDDLE  ALT=\"-%281%2F+16%29x%5E2+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The standard form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+h%29%5E2+=+4p+%28y+-+k%29 ALIGN=MIDDLE  ALT=\"%28x+-+h%29%5E2+=+4p+%28y+-+k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where the focus is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+%2B+p ALIGN=MIDDLE  ALT=\"+k+%2B+p\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and the directrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k+-+p ALIGN=MIDDLE  ALT=\"y+=+k+-+p\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "given: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F+16%29x%5E2+=+y ALIGN=MIDDLE  ALT=\"-%281%2F+16%29x%5E2+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+%281%2F%281%2F-16%29%29y ALIGN=MIDDLE  ALT=\"x%5E2+=+%281%2F%281%2F-16%29%29y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+-16y ALIGN=MIDDLE  ALT=\"x%5E2+=+-16y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0 ALIGN=MIDDLE  ALT=\"k=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>the vertex at:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4p=-16 ALIGN=MIDDLE  ALT=\"+4p=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-4 ALIGN=MIDDLE  ALT=\"p=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "a focus at  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+%2B+p ALIGN=MIDDLE  ALT=\"k+%2B+p\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
document.write( "\n" );
document.write( "a directrix at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k-p ALIGN=MIDDLE  ALT=\"y+=+k-p\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0+-+%28-4%29=4 ALIGN=MIDDLE  ALT=\"y=0+-+%28-4%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "The focal width of a parabola is the length of a segment that is parallel to the directrix and passing through the focus of a parabola. The length of this segment is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p ALIGN=MIDDLE  ALT=\"4p\"   DISABLED_style= \"max-width:90%; height:auto;\" > units, or four time the length from the focus to the vertex.\r<BR>\n" );
document.write( "\n" );
document.write( "focal width:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "answer:Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );