document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=752890>Question 752890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you write out an equation for a parabola with the vertex (0,0) and a focus (0, -1/12)? \r<BR>\n" );
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document.write( "i have tried to fit it in the equation (x-h)^2+(y-k)^2=r^2, but i got a completely off- answer... \r<BR>\n" );
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document.write( "I looked up the answer key online, and it said that the answer is  \" y = -3x^2 \" , but i am NOT  getting even close.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #458113 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=458113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The model you tried to fit did not work because that is a form of equation for a circle.  \r<BR>\n" );
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document.write( "When you use the definition of a parabola to derive an equation, using a focal distance p from the vertex, you get a general equation <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;\" >.  This is a parabola with vertex on the origin, and vertex at a minimum. This derived equation can equivalently be written <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F%284p%29%29x%5E2 ALIGN=MIDDLE  ALT=\"y=%281%2F%284p%29%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  In your case, seeing the vertex is (0,0) and the focus is (0,-1/12), you should be able to know the value for p for the model.  If you SEE this value for p, then good!  Put in the values into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%281%2F%284p%29%29x%5E2%29 ALIGN=MIDDLE  ALT=\"y=%28%281%2F%284p%29%29x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify.\r<BR>\n" );
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document.write( "This should now be obvious.  Vertex is (0,0) and focus (0,-1/12).  p=1/12, and because the parabola opens DOWNWARD, the coefficient on x^2 must be LESS THAN ZERO, so you show a negative sign (instead of implying a positive sign).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2A%281%2F%284%2A%281%2F12%29%29%29x%5E2 ALIGN=MIDDLE  ALT=\"y=-1%2A%281%2F%284%2A%281%2F12%29%29%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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