document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=747686>Question 747686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write and equation for the parabola with a vertex (0,0) and focus (0,-1/12)<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 #455104 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=455104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The focus is below the vertex, so this vertex is a maximum.  You expect the coefficient on x^2 to be negative.  \r<BR>\n" );
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document.write( "A general equation for a parabola having vertex on the origin is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4py=x%5E2 ALIGN=MIDDLE  ALT=\"4py=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where p is the focal length, distance between the focus and the vertex.  In your exercise, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1%2F12 ALIGN=MIDDLE  ALT=\"p=1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  See your textbook and http://en.wikipedia.org/wiki/Parabola .\r<BR>\n" );
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document.write( "The equation for the described parabola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%281%2F%284%2Ap%29%29%2Ax%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%281%2F%284%2Ap%29%29%2Ax%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and as said, since the vertex is a maximum, we must have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%284p%29%29%3C0 ALIGN=MIDDLE  ALT=\"%281%2F%284p%29%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F%284%2A%281%2F12%29%29%29x%5E2 ALIGN=MIDDLE  ALT=\"y=-%281%2F%284%2A%281%2F12%29%29%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%2812%2F4%29x%5E2 ALIGN=MIDDLE  ALT=\"y=-%2812%2F4%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-3x%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-3x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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