document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001602>Question 1001602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation:\r<BR>\n" );
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document.write( "Vertex is (5,4)\r<BR>\n" );
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document.write( "Focus is (8,4) </SPAN>\n" );
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document.write( "Write an equation of the parabola with vertex (3, 1) and focus (3, 5).\r<BR>\n" );
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document.write( " Write an equation:<BR>\n" );
document.write( "Vertex is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Focus is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
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document.write( "The equation of a parabola with vertex (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is either\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+h%29%5E2+=+4p%28y+-+k%29+ ALIGN=MIDDLE  ALT=\"%28x+-+h%29%5E2+=+4p%28y+-+k%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+k%29%5E2+=+4p%28x+-+h%29 ALIGN=MIDDLE  ALT=\"%28y+-+k%29%5E2+=+4p%28x+-+h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where the vertex is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >),  <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 distance from vertex to focus \r<BR>\n" );
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document.write( "Since the vertex is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+5 ALIGN=MIDDLE  ALT=\"h+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+4 ALIGN=MIDDLE  ALT=\"k+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since the vertex (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and focus (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) have the same y-coordinate, it is equation of the second type.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+k%29%5E2+=+4p%28x+-+h%29 ALIGN=MIDDLE  ALT=\"%28y+-+k%29%5E2+=+4p%28x+-+h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The distance from vertex to focus is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > units. Since the focus is right of the vertex, <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, and so <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;\" >. (Parabola opens to the right)\r<BR>\n" );
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document.write( "So the equation is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+4%29%5E2+=+4%2A3%28x+-+5%29 ALIGN=MIDDLE  ALT=\"%28y+-+4%29%5E2+=+4%2A3%28x+-+5%29\"   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=%28y+-+4%29%5E2+=+12%28x+-+5%29 ALIGN=MIDDLE  ALT=\"%28y+-+4%29%5E2+=+12%28x+-+5%29\"   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=%28y+-+4%29%5E2%2F12+=+x+-+5 ALIGN=MIDDLE  ALT=\"%28y+-+4%29%5E2%2F12+=+x+-+5\"   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=%281%2F12%29%28y+-+4%29%5E2%2B5+=+x+ ALIGN=MIDDLE  ALT=\"%281%2F12%29%28y+-+4%29%5E2%2B5+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "it cannot be this:<BR>\n" );
document.write( "x= 1/4c y^2 (x-h)^2  + k....here is something wrong\r<BR>\n" );
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document.write( " </SPAN>\n" );
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