document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972479>Question 972479</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The vertex,focus and directrix of the parabola y^2+4x-16y+8=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594863 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=594863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A reference model for a horizontal parabola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4px=y%5E2 ALIGN=MIDDLE  ALT=\"4px=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and allowing for translations of location,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%28x-h%29=%28y-k%29%5E2 ALIGN=MIDDLE  ALT=\"4p%28x-h%29=%28y-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  These forms come from the derivation for the equation of a parabola.  The meaning of p is the distance between the vertex (for standard position) and either the focus or the directrix.\r<BR>\n" );
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document.write( "Start from the general given equation, complete the square, and put into STANDARD FORM.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-16y=-4x-8 ALIGN=MIDDLE  ALT=\"y%5E2-16y=-4x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-16y%2B64=-4x-8%2B64 ALIGN=MIDDLE  ALT=\"y%5E2-16y%2B64=-4x-8%2B64\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the constant, 64 needed for completing the square for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-8%29%5E2=-4x%2B56 ALIGN=MIDDLE  ALT=\"%28y-8%29%5E2=-4x%2B56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28y-8%29%5E2=4%28x-14%29 ALIGN=MIDDLE  ALT=\"-%28y-8%29%5E2=4%28x-14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28x-14%29=%28y-8%29%5E2 ALIGN=MIDDLE  ALT=\"-4%28x-14%29=%28y-8%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------still not exactly standard form, but <b>vertex is (14,8)</b>,  then corresponding coefficients gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p=-4 ALIGN=MIDDLE  ALT=\"4p=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-1 ALIGN=MIDDLE  ALT=\"p=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The vertex occurs as a maximum for x value so the parabola opens to the left, and therefore the focus is 1 unit to the left of the vertex.<BR>\n" );
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document.write( "Focus is (13,8);<BR>\n" );
document.write( "Directrix is x=15.<BR>\n" );
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