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 #458115 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=458115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:<BR>\n" );
document.write( " the vertex (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and a focus (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F12 ALIGN=MIDDLE  ALT=\"-1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "The directed distance from the vertex to the focus is called <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the \"parabolic constant\".  If going from vertex to focus is an upward or rightward motion, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p ALIGN=MIDDLE  ALT=\"+p\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive.  If downward  or leftward, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+ ALIGN=MIDDLE  ALT=\"p+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative.  Here <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative, in fact,it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F12 ALIGN=MIDDLE  ALT=\"-1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > because going from the vertex (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) to the focus.\r<BR>\n" );
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document.write( "The value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F12 ALIGN=MIDDLE  ALT=\"-1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since that is the directed distance from the vertex to the focus. Since the axis is vertical, the general equation is  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+4px%5E2+ ALIGN=MIDDLE  ALT=\"y=+4px%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " So your equation is :\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4%28+-1%2F12%29x%5E2+ ALIGN=MIDDLE  ALT=\"y+=+4%28+-1%2F12%29x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=-3x%5E2+ ALIGN=MIDDLE  ALT=\"y+=-3x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C600%2C+-5%2C+5%2C+-10%2C+5%2C+-3x%5E2%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C600%2C+-5%2C+5%2C+-10%2C+5%2C+-3x%5E2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
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