document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=715317>Question 715317</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I basically have a general question. I am trying to use information provided to write the transformational equation of each parabola. I am given the vertex and focus and the vertex and directrix. I know how to find p but I do not where to put it and when the x is squared vs the y being squared. I guess I need the rules?\r<BR>\n" );
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document.write( "Example: Vertex: (-7,-8) Focus: (47/8,8)<BR>\n" );
document.write( "Knowing that the Vertex is (h,k)...<BR>\n" );
document.write( "I take the absolute value of 6-(47/8)=(1/8)... (1/8) is the value of p<BR>\n" );
document.write( "4*(1/8)= .5<BR>\n" );
document.write( "After that I am lost... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #439377 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=439377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I basically have a general question. I am trying to use information provided to write the transformational equation of each parabola. I am given the vertex and focus and the vertex and directrix. I know how to find p but I do not where to put it and when the x is squared vs the y being squared. I guess I need the rules? <BR>\n" );
document.write( "Example: Vertex: (6,8) Focus: (47/8,8)<BR>\n" );
document.write( "Knowing that the Vertex is (h,k)...<BR>\n" );
document.write( "I take the absolute value of 6-(47/8)=(1/8)... (1/8) is the value of p<BR>\n" );
document.write( "4*(1/8)= .5<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Rules:<BR>\n" );
document.write( "In the form 4p(y-k) = (x-h)^2 the vertex is (h,k)<BR>\n" );
document.write( "If \"4p\" is positive the parabola opens up.<BR>\n" );
document.write( "If \"4p\" is negative the parabola opens down.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "\"P\" is the distance from the vertex to the focus<BR>\n" );
document.write( "AND<BR>\n" );
document.write( "\"p\" is the distance from the vertex to the directrix.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "In the form 4p(x-h) = (y-k)^2 the vertex is (h,k)<BR>\n" );
document.write( "If \"4p\" is positive the parabola opens to the right<BR>\n" );
document.write( "If \"4p\" is negative the parabola opens to the left.<BR>\n" );
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document.write( "Your Problem:<BR>\n" );
document.write( "Vertex at (6,8) so h = 6 and k = 8<BR>\n" );
document.write( "p = 1/8, so 4p = 1/2<BR>\n" );
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document.write( "Since the vertex and the focus have the same y-value<BR>\n" );
document.write( "the axis of symmetry is a y-line, or is horizontal.<BR>\n" );
document.write( "Note: Notice that the focus is 1/8 to the left of the vertex,<BR>\n" );
document.write( "so your parabola must be opening to the left.<BR>\n" );
document.write( "Since the focus is to the left of the vertex, p is negative,<BR>\n" );
document.write( "so 4p is negative.\r<BR>\n" );
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document.write( "(-1/2)(x-6) = (y-8)^2<BR>\n" );
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document.write( "The directrix is |p| to the right the vertex:<BR>\n" );
document.write( "x = 6 1/8<BR>\n" );
document.write( "====================== <BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "========================<BR>\n" );
document.write( " </SPAN>\n" );
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