document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189988>Question 189988</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.   Choose the equation of the parabola with a vertex at the origin and a focus at (0, –3).\r<BR>\n" );
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document.write( "1. y=-1/3x<BR>\n" );
document.write( "2. y=1/12x^2<BR>\n" );
document.write( "3. y=-1/3x^2<BR>\n" );
document.write( "4. y=1/12x^2<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 #142686 by </B><A HREF=/tutors/aboutme.mpl?userid=cutepiscean5><B>cutepiscean5(19)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=cutepiscean5><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=142686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "we have the vertex as (0,0) and focus as (0,-3) , since the x-coordinate of both the vertex and focus are the same, it means the parabola is a vertical parabola.\r<BR>\n" );
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document.write( "The form of a vertical parabola is given by:\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "where (h,k) is the vertex (here it is (0,0))<BR>\n" );
document.write( "p = distance between the vertex and the focus of the parabola.\r<BR>\n" );
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document.write( "we are given the coordinates of focus as (0,-3), thus the y-coordinate here is equivalent to k + p\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3+=+0+%2B+p+ ALIGN=MIDDLE  ALT=\"+-3+=+0+%2B+p+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+-3+ ALIGN=MIDDLE  ALT=\"+p+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we plug in all the values into the equation and get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2A%28-3%29%28y-0%29+=+%28x-0%29%5E2+ ALIGN=MIDDLE  ALT=\"+4%2A%28-3%29%28y-0%29+=+%28x-0%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplifying further we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12%2Ay+=+x%5E2+ ALIGN=MIDDLE  ALT=\"+-12%2Ay+=+x%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+=+-1%2F12%2Ax%5E2+ ALIGN=MIDDLE  ALT=\"+y+=+-1%2F12%2Ax%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so out of choices 2 and 4 which ever corresponds to our answer is the correct one. (there is a misprint in the choices that has been given for 2 and 4)\r<BR>\n" );
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document.write( "Hope this helps you. </SPAN>\n" );
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