document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201701>Question 1201701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation of a parabola is 12 y = ( x − 1 ) 2 − 48 12y=(x-1)2-48 . Identify the vertex, focus, and directrix of the parabola. ​  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836193 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=836193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
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document.write( "NOTE for future reference: the symbol \"^\" (shift-6) is commonly used to represent exponents.  So you can write the equation for this problem as<br><BR>\n" );
document.write( "12y=(x-1)^2-48<BR>\n" );
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document.write( "The x term is squared, so the graph opens up or down.  The general vertex form of the equation of a parabola I prefer to use is this:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-k=%281%2F%284p%29%29%28x-h%29%5E2 ALIGN=MIDDLE  ALT=\"y-k=%281%2F%284p%29%29%28x-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Note many references will show this equation in different equivalent forms; and different students have different preferences on which form to use.  Some common equivalent forms are<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F%284p%29%29%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=%281%2F%284p%29%29%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [puts only \"y\" on the left]<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%28y-k%29=%28x-h%29%5E2 ALIGN=MIDDLE  ALT=\"4p%28y-k%29=%28x-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [keeps the \"4p\" on the left so it is not a fraction]<br><BR>\n" );
document.write( "In any of those forms, the vertex is (h,k); p is the directed distance (i.e., can be negative) from the directrix to the vertex and from the vertex to the focus.<br><BR>\n" );
document.write( "Put the equation in your example in this form:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y=%28x-1%29%5E2-48 ALIGN=MIDDLE  ALT=\"12y=%28x-1%29%5E2-48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y%2B48=%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"12y%2B48=%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28y%2B4%29=%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"12%28y%2B4%29=%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4=%281%2F12%29%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"y%2B4=%281%2F12%29%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28-4%29=%281%2F%284%2A3%29%29%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"y-%28-4%29=%281%2F%284%2A3%29%29%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The vertex is (1,-4) and p is 3.<br><BR>\n" );
document.write( "The directrix is p = 3 units below the vertex, at y = -7.<br><BR>\n" );
document.write( "The focus is p = 3 units above the vertex, at (1,-1).<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "vertex (1,-4)<BR>\n" );
document.write( "focus (1,-1)<BR>\n" );
document.write( "directrix y = -7<br><BR>\n" );
document.write( " </SPAN>\n" );
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