document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204031>Question 1204031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a parabola opens upward, has focus at (1,-1), has a horizontal directrix, and passes through the point (-31,59).\r<BR>\n" );
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document.write( "a. The directrix will have an equation of?\r<BR>\n" );
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document.write( "b. The equation of the parabola will be?<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 #840036 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=840036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "If the parabola is vertical, the equation of the parabola is of the form \r<BR>\n" );
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document.write( ".<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%28x+-+h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"+y+=+a%28x+-+h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Focus (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)= (<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+%2B+1%2F%284a%29+ ALIGN=MIDDLE  ALT=\"k+%2B+1%2F%284a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=1 ALIGN=MIDDLE  ALT=\"h=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+%2B+1%2F%284a%29=-1 ALIGN=MIDDLE  ALT=\"k+%2B+1%2F%284a%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-1-1%2F%284a%29 ALIGN=MIDDLE  ALT=\"k=-1-1%2F%284a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Directrix have an equation:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k+-+1%2F%284a%29 ALIGN=MIDDLE  ALT=\"y+=+k+-+1%2F%284a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1-1%2F%284a%29-+1%2F%284a%29 ALIGN=MIDDLE  ALT=\"y=-1-1%2F%284a%29-+1%2F%284a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2F%282+a%29+-+1 ALIGN=MIDDLE  ALT=\"y=-1%2F%282+a%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "passes through the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-31 ALIGN=MIDDLE  ALT=\"-31\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=59 ALIGN=MIDDLE  ALT=\"59\"   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=59+=+a%28-31+-+1%29%5E2+%2B+-1-1%2F%284a%29 ALIGN=MIDDLE  ALT=\"59+=+a%28-31+-+1%29%5E2+%2B+-1-1%2F%284a%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=a+=+-1%2F256 ALIGN=MIDDLE  ALT=\"a+=+-1%2F256\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1%2F16 ALIGN=MIDDLE  ALT=\"a=1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since given that parabola opens up, we need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1%2F16 ALIGN=MIDDLE  ALT=\"a=1%2F16\"   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=k=-1-1%2F%284%281%2F16%29%29=-5 ALIGN=MIDDLE  ALT=\"k=-1-1%2F%284%281%2F16%29%29=-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=y=-1%2F%282%281%2F16%29%29+-+1=-9 ALIGN=MIDDLE  ALT=\"y=-1%2F%282%281%2F16%29%29+-+1=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a. The directrix will have an equation of\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-9 ALIGN=MIDDLE  ALT=\"y=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. The equation of the parabola will be?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F16%29%28x+-+1%29%5E2+-5 ALIGN=MIDDLE  ALT=\"y+=+%281%2F16%29%28x+-+1%29%5E2+-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=+drawing%28+600%2C+600%2C+-60%2C+60%2C+-60%2C+60%2C%0D%0Acircle%281%2C-1%2C.25%29%2Clocate+%281%2C-1%2CF%281%2C-1%29%29%2C%0D%0Acircle%28-31%2C59%2C.25%29%2Clocate+%28-31%2C59%2Cp%28-31%2C59%29%29%2C%0D%0A%0D%0Agraph%28+600%2C+600%2C+-60%2C+60%2C+-60%2C+60%2C+%281%2F16%29%28x+-+1%29%5E2+-5%2C-9%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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