document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089163>Question 1089163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> convert the equation to standard for by completing the square on x. Then find the vertex, focus and directrix of the parabola. then graph\r<BR>\n" );
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document.write( "x^2+2x-8y-31=0<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 #703511 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=703511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-8y-31=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-8y-31=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The \"vertex\" form of a parabola with its vertex at (<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:\r<BR>\n" );
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document.write( "regular: <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;\" ><BR>\n" );
document.write( "sideways: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+a%28y+-k%29%5E2+%2B+h+ ALIGN=MIDDLE  ALT=\"x+=+a%28y+-k%29%5E2+%2B+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The conics form of the parabola equation (the one you'll find in advanced or older texts) is:\r<BR>\n" );
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document.write( "    regular: <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;\" ><BR>\n" );
document.write( "    sideways: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%28x+-h%29+=+%28y+-k%29%5E2 ALIGN=MIDDLE  ALT=\"4p%28x+-h%29+=+%28y+-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p ALIGN=MIDDLE  ALT=\"4p\"   DISABLED_style= \"max-width:90%; height:auto;\" > is actually the same as the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4a ALIGN=MIDDLE  ALT=\"1%2F4a\"   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=%28x%5E2%2B2x%2Bb%5E2%29-b%5E2-31=8y ALIGN=MIDDLE  ALT=\"%28x%5E2%2B2x%2Bb%5E2%29-b%5E2-31=8y\"   DISABLED_style= \"max-width:90%; height:auto;\" >....since coefficients <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=2 ALIGN=MIDDLE  ALT=\"2ab=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A1%2Ab=2 ALIGN=MIDDLE  ALT=\"2%2A1%2Ab=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=2 ALIGN=MIDDLE  ALT=\"2b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   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=8y=%28x%5E2%2B2x%2B1%5E2%29-1%5E2-31 ALIGN=MIDDLE  ALT=\"8y=%28x%5E2%2B2x%2B1%5E2%29-1%5E2-31\"   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=8y=%28x%2B1%29%5E2-1-31 ALIGN=MIDDLE  ALT=\"8y=%28x%2B1%29%5E2-1-31\"   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=%281%2F8%29%28x%2B1%29%5E2-32%2F8 ALIGN=MIDDLE  ALT=\"y=%281%2F8%29%28x%2B1%29%5E2-32%2F8\"   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=%281%2F8%29%28x%2B1%29%5E2-4 ALIGN=MIDDLE  ALT=\"y=%281%2F8%29%28x%2B1%29%5E2-4\"   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;\" > 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;\" >, and \r<BR>\n" );
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document.write( "the vertex is at (<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=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "The focus is \"p\" units from the vertex:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=1%2F4a=1%2F%284%281%2F8%29%29=2 ALIGN=MIDDLE  ALT=\"p+=1%2F4a=1%2F%284%281%2F8%29%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
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document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2 ALIGN=MIDDLE  ALT=\"p=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then, <BR>\n" );
document.write( "the focus is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > unit above the vertex, at  (<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=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >), <BR>\n" );
document.write( "and the directrix is the horizontal line<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-6 ALIGN=MIDDLE  ALT=\"+y+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, p or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=two ALIGN=MIDDLE  ALT=\"two\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+units ALIGN=MIDDLE  ALT=\"+units\"   DISABLED_style= \"max-width:90%; height:auto;\" > below the vertex\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+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%28-1%2C-4%2C.12%29%2Ccircle%28-1%2C-2%2C.12%29%2C%0D%0Alocate%28-1%2C-4%2CV%28-1%2C-4%29%29%2Clocate%28-1%2C-2%2Cf%28-1%2C-2%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F8%29%28x%2B1%29%5E2-4%2C-6%2C-6%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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