document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198581>Question 1198581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the vertex, focus, and directrix for (y+3)^2=4(x-3).<BR>\n" );
document.write( "One of the following is the correct answer. Which one?\r<BR>\n" );
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document.write( "A) the vertex is (-3,3), the focus is (4,-3),and the directrix is x=2<BR>\n" );
document.write( "B) the vertex is (3,-3), the focus is (-4,3),and the directrix is x=2<BR>\n" );
document.write( "C) the vertex is (3,-3), the focus is (4,-3),and the directrix is x=2<BR>\n" );
document.write( "D) the vertex is (-3,3), the focus is (-4,3),and the directrix is x=-2<BR>\n" );
document.write( "E)the vertex is (3,-3), the focus is (4,-3),and the directrix is x=-2<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832192 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832192\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Basic vertex form:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2=%284p%29%28x-h%29 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2=%284p%29%28x-h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In that form, the vertex is (h,k), and p is the directed distance (i.e., could be negative) from the directrix to the focus and from the focus to the vertex.  The y term is squared, so the parabola opens right or left.<br><BR>\n" );
document.write( "In your example, the vertex (h,k) is (3,-3); and 4p=4, so p=1.  So the focus is 1 unit to the right of the vertex, at (4,-3); and the directrix is 1 unit to the left of the vertex, at x=2.<br><BR>\n" );
document.write( "ANSWER: C)<br><BR>\n" );
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document.write( "Side note:<br><BR>\n" );
document.write( "I personally prefer the equivalent basic vertex form,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29=%281%2F%284p%29%29%28y-k%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29=%281%2F%284p%29%29%28y-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "because I prefer having the linear expression on the left side of the equation.<br><BR>\n" );
document.write( "But of course they are equivalent, so either form is fine.<br><BR>\n" );
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