document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190797>Question 1190797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the parabola with vertex on Oy, axis parallel to Ox, and passing<BR>\n" );
document.write( "through (2, 2) and (8, -1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822550 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=822550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( " axis parallel to Ox=>your parabola opens right/left\r<BR>\n" );
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document.write( "Vertex form: \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( "vertex on O<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   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-k%29%5E2=4p%28x-0%29 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2=4p%28x-0%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-k%29%5E2=4px ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2=4px\"   DISABLED_style= \"max-width:90%; height:auto;\" >............passing through (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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;\" >) , use it to calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   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=%282-k%29%5E2=4p%2A2 ALIGN=MIDDLE  ALT=\"%282-k%29%5E2=4p%2A2\"   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%5E2+-+4+k+%2B+4=8p ALIGN=MIDDLE  ALT=\"k%5E2+-+4+k+%2B+4=8p\"   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=p=+%28k%5E2+-+4+k+%2B+4%29%2F8 ALIGN=MIDDLE  ALT=\"p=+%28k%5E2+-+4+k+%2B+4%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........1)\r<BR>\n" );
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document.write( "passing through (<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=-1 ALIGN=MIDDLE  ALT=\"-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=%28-1-k%29%5E2=4p%2A8 ALIGN=MIDDLE  ALT=\"%28-1-k%29%5E2=4p%2A8\"   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%5E2+%2B+2+k+%2B+1=32p ALIGN=MIDDLE  ALT=\"k%5E2+%2B+2+k+%2B+1=32p\"   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=p=%28k%5E2+%2B+2+k+%2B+1%29%2F32 ALIGN=MIDDLE  ALT=\"p=%28k%5E2+%2B+2+k+%2B+1%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........2)\r<BR>\n" );
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document.write( "from 1) and 2) we have\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%5E2+-+4+k+%2B+4%29%2F8=%28k%5E2+%2B+2+k+%2B+1%29%2F32 ALIGN=MIDDLE  ALT=\"%28k%5E2+-+4+k+%2B+4%29%2F8=%28k%5E2+%2B+2+k+%2B+1%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%28k%5E2+-+4+k+%2B+4%29=8%28k%5E2+%2B+2+k+%2B+1%29 ALIGN=MIDDLE  ALT=\"32%28k%5E2+-+4+k+%2B+4%29=8%28k%5E2+%2B+2+k+%2B+1%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=32+k%5E2+-+128+k+%2B+128-8k%5E2+-+16+k+-8=0 ALIGN=MIDDLE  ALT=\"32+k%5E2+-+128+k+%2B+128-8k%5E2+-+16+k+-8=0\"   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=24+k%5E2+-+144+k+%2B+120=0 ALIGN=MIDDLE  ALT=\"24+k%5E2+-+144+k+%2B+120=0\"   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=24+%28k%5E2+-+6k+%2B+5%29=0 ALIGN=MIDDLE  ALT=\"24+%28k%5E2+-+6k+%2B+5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24+%28%28k+-+1%29+%28k+-+5%29%29=0 ALIGN=MIDDLE  ALT=\"24+%28%28k+-+1%29+%28k+-+5%29%29=0\"   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+ ALIGN=MIDDLE  ALT=\"k=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=5 ALIGN=MIDDLE  ALT=\"k=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=1 ALIGN=MIDDLE  ALT=\"k=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+%281%5E2+-+4%2A1+%2B+4%29%2F8 ALIGN=MIDDLE  ALT=\"p=+%281%5E2+-+4%2A1+%2B+4%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+1%2F8 ALIGN=MIDDLE  ALT=\"p=+1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=5 ALIGN=MIDDLE  ALT=\"k=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=+%285%5E2+-+4%2A5+%2B+4%29%2F8 ALIGN=MIDDLE  ALT=\"p=+%285%5E2+-+4%2A5+%2B+4%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=9%2F8 ALIGN=MIDDLE  ALT=\"p=9%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and your equations are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-1%29%5E2=4%281%2F8%29x ALIGN=MIDDLE  ALT=\"%28y-1%29%5E2=4%281%2F8%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-1%29%5E2=%281%2F2%29x ALIGN=MIDDLE  ALT=\"%28y-1%29%5E2=%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........1\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=%28y-5%29%5E2=4%289%2F8%29x ALIGN=MIDDLE  ALT=\"%28y-5%29%5E2=4%289%2F8%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-5%29%5E2=%289%2F2%29x ALIGN=MIDDLE  ALT=\"%28y-5%29%5E2=%289%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........2\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );