document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039252>Question 1039252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PARABOLA: what's the vertex, focus, directrix, latus rectum and graph of the y^2+16x=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #653998 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=653998\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Put the equation into vertex form.  Since the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> variable is squared, this is a parabola with a horizontal axis of symmetry and a vertical directrix.  Vertex form for such a parabola is the equation solved for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> in terms of everything else.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ -\frac{1}{16}y^2\">\r<BR>\n" );
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document.write( "Rewrite so that the elements of the vertex form are evident:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ -\frac{1}{16}(y\ -\ 0)^2\ +\ 0\">\r<BR>\n" );
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document.write( "The general form of a parabola with a horizontal axis is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ a(y\ -\ k)^2\ +\ h\">\r<BR>\n" );
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document.write( "Which is a parabola with a horizontal axis, \r<BR>\n" );
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document.write( "vertex at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (h,\,k)\">, <BR>\n" );
document.write( "parameter <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\ =\ \frac{1}{4a}\">, <BR>\n" );
document.write( "directrix equation: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ h\ -\ p\">, <BR>\n" );
document.write( "focus at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (h\ +\ p, k)\">, <BR>\n" );
document.write( "and latus rectum endpoints at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (h\ +\ p,k\ \pm\ 2p)\">.\r<BR>\n" );
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document.write( "I'll help you find the parameter <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ =\ -\frac{1}{16}\ \Rightarrow\ 4a\ =\ -\frac{1}{4}\ \Rightarrow\ \frac{1}{4a}\ =\ -4\ =\ p\">\r<BR>\n" );
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document.write( "The rest is just plugging in numbers.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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