document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143057>Question 1143057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the parabola in standard form and determine its vertex, focus, directrix, and axis. <BR>\n" );
document.write( "  2<BR>\n" );
document.write( "y   +4x -8y +28=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763825 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=763825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I will guess that you want vertex form, since that is the form that tells you the most about the parabola.<br><BR>\n" );
document.write( "The squared term is y, so the parabola opens right or left.  The vertex form of the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2F%284p%29%29%28y-k%29%5E2%2Bh ALIGN=MIDDLE  ALT=\"x+=+%281%2F%284p%29%29%28y-k%29%5E2%2Bh\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "where the vertex is (h,k) and p is the directed distance from the directrix to the vertex and from the vertex to the focus.<br><BR>\n" );
document.write( "Put the given equation in that form by completing the square and solving for x.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B4x-8y%2B28+=+0 ALIGN=MIDDLE  ALT=\"y%5E2%2B4x-8y%2B28+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-8y+=+-4x-28 ALIGN=MIDDLE  ALT=\"y%5E2-8y+=+-4x-28\"   DISABLED_style= \"max-width:90%; height:auto;\" >       isolate the y terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-8y%2B16+=+-4x-12 ALIGN=MIDDLE  ALT=\"y%5E2-8y%2B16+=+-4x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >    complete the square in y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-4%29%5E2+=+-4x-12 ALIGN=MIDDLE  ALT=\"%28y-4%29%5E2+=+-4x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+-%28y-4%29%5E2-12 ALIGN=MIDDLE  ALT=\"4x+=+-%28y-4%29%5E2-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >      isolate the x term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1%2F4%29%28y-4%29%5E2-3 ALIGN=MIDDLE  ALT=\"x+=+%28-1%2F4%29%28y-4%29%5E2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >   solve for x<br><BR>\n" );
document.write( "This is in vertex form, so the vertex is (-3,4).<br><BR>\n" );
document.write( "The coefficient (-1/4) is 1/(4p), so p is -1.  That means the focus is 1 unit to the left of the vertex and the directrix is 1 unit to the right of the vertex.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1%2F4%29%28y-4%29%5E2-3 ALIGN=MIDDLE  ALT=\"x+=+%28-1%2F4%29%28y-4%29%5E2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "vertex: (-3,4)<BR>\n" );
document.write( "focus: (-4,4)<BR>\n" );
document.write( "directrix: x=-2<BR>\n" );
document.write( "axis: y=4<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );