document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997627>Question 997627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the vertex, value of p, axis of symmetry, focus, and directrix of each parabola with the equation X-1=-1/12y^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615646 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=615646\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation written correctly, or in more precise manner is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=-%281%2F12%29y%5E2 ALIGN=MIDDLE  ALT=\"x-1=-%281%2F12%29y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This is a parabola with symmetry axis parallel to the x-axis, and graph of parabola opens to the left, as indicated by coefficient  NEGATIVE  1/12.  This coefficient  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F12 ALIGN=MIDDLE  ALT=\"-1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > tells you information about how far is focus and directrix from the vertex.  YOUR equation's vertex is  (1,0).\r<BR>\n" );
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document.write( "Learn better how this works through these two videos:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"https://www.youtube.com/watch?v=M8LGsQMwwj4\">Derive equation for parabola from focus and directrix</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"https://www.youtube.com/watch?v=Wworlx39KfQ\">Equation for parabola from directrix and focus but vertex is NOT at the Origin</a>\r<BR>\n" );
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document.write( "According to the form of the equation used in the derivations,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p=%281%2F12%29 ALIGN=MIDDLE  ALT=\"4p=%281%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and |p| is how far vertex is from either focus or directrix.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%281%2F4%29%281%2F12%29 ALIGN=MIDDLE  ALT=\"p=%281%2F4%29%281%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1%2F48 ALIGN=MIDDLE  ALT=\"p=1%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Focus is on the concave side, to left of the vertex.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1-1%2F48 ALIGN=MIDDLE  ALT=\"x=1-1%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=48%2F48-1%2F48 ALIGN=MIDDLE  ALT=\"x=48%2F48-1%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=47%2F48 ALIGN=MIDDLE  ALT=\"x=47%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this y-value unchanged.<BR>\n" );
document.write( "FOCUS:   ( 47/48, 0 )\r<BR>\n" );
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document.write( "Directrix would be on the other side and is the vertical line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%261%2F48 ALIGN=MIDDLE  ALT=\"x=1%261%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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