document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160185>Question 1160185</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write the equation of a parabola with a vertex at the origin and a focus of (0, -3). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #783393 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=783393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The vertex form of the equation of a parabola that opens up or down with vertex (h,k) is<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( "where p is the directed distance (that is, it might be negative) from the vertex to the focus.<br><BR>\n" );
document.write( "In this problem, all the information required to write the equation is given to you; there is no work to be done other than plug in the numbers.<br><BR>\n" );
document.write( "The vertex is (0,0); the directed distance from the vertex (0,0) to the focus (0,-3) is -3, so p = -3.<br><BR>\n" );
document.write( "Plug in the numbers:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28-3%29+=+%281%2F%284%28-3%29%29%29%28x-0%29%5E2 ALIGN=MIDDLE  ALT=\"y-%28-3%29+=+%281%2F%284%28-3%29%29%29%28x-0%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%2B3+=+%28-1%2F12%29x%5E2 ALIGN=MIDDLE  ALT=\"y%2B3+=+%28-1%2F12%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "-------------------------------------------<br><BR>\n" );
document.write( "Oops!  Tutor @MathTherapy spotted my error....  The vertex is (0,0), not (0,-3). So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-0+=+%281%2F%284%28-3%29%29%29%28x-0%29%5E2 ALIGN=MIDDLE  ALT=\"y-0+=+%281%2F%284%28-3%29%29%29%28x-0%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+=+%28-1%2F12%29x%5E2 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F12%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );