document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198612>Question 1198612</A>: <I><SPAN STYLE=\"word-break: break-all;\"> give the standard equation of (3x-2)^2=84y-12. Provide it's vertex, focus, directrix, axis of symmetry, latus rectum and endpoints of latus rectum. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832237 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=832237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we use the standard form \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( "for parabolas that have an axis of symmetry parallel to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >-axis\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-2%29%5E2=84y-12 ALIGN=MIDDLE  ALT=\"%283x-2%29%5E2=84y-12\"   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=9x%5E2+-+12x+%2B+4=84y-12 ALIGN=MIDDLE  ALT=\"9x%5E2+-+12x+%2B+4=84y-12\"   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=9x%5E2+-+12x+=84y-12-4 ALIGN=MIDDLE  ALT=\"9x%5E2+-+12x+=84y-12-4\"   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=9%28x%5E2+-+%2812%2F9%29x%29+=84y-16 ALIGN=MIDDLE  ALT=\"9%28x%5E2+-+%2812%2F9%29x%29+=84y-16\"   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=9%28x%5E2+-+%284%2F3%29x%2B%284%2F6%29%5E2%29+-9%284%2F6%29%5E2=84y-16 ALIGN=MIDDLE  ALT=\"9%28x%5E2+-+%284%2F3%29x%2B%284%2F6%29%5E2%29+-9%284%2F6%29%5E2=84y-16\"   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=9%28x%5E2+-+%284%2F3%29x%2B%282%2F3%29%5E2%29+-9%282%2F3%29%5E2=84y-16 ALIGN=MIDDLE  ALT=\"9%28x%5E2+-+%284%2F3%29x%2B%282%2F3%29%5E2%29+-9%282%2F3%29%5E2=84y-16\"   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=9%28x+-+2%2F3%29%5E2+-4=84y-16 ALIGN=MIDDLE  ALT=\"9%28x+-+2%2F3%29%5E2+-4=84y-16\"   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=9%28x+-+2%2F3%29%5E2+=84y-16%2B4 ALIGN=MIDDLE  ALT=\"9%28x+-+2%2F3%29%5E2+=84y-16%2B4\"   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=9%28x+-+2%2F3%29%5E2+=84y-12 ALIGN=MIDDLE  ALT=\"9%28x+-+2%2F3%29%5E2+=84y-12\"   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=9%28x+-+2%2F3%29%5E2+=84%28y-12%2F84%29 ALIGN=MIDDLE  ALT=\"9%28x+-+2%2F3%29%5E2+=84%28y-12%2F84%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=9%28x+-+2%2F3%29%5E2+=84%28y-1%2F7%29 ALIGN=MIDDLE  ALT=\"9%28x+-+2%2F3%29%5E2+=84%28y-1%2F7%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=%28x+-+2%2F3%29%5E2+=%2884%2F9%29%28y-1%2F7%29 ALIGN=MIDDLE  ALT=\"%28x+-+2%2F3%29%5E2+=%2884%2F9%29%28y-1%2F7%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=%28x+-+2%2F3%29%5E2+=%2828%2F3%29%28y-1%2F7%29 ALIGN=MIDDLE  ALT=\"%28x+-+2%2F3%29%5E2+=%2828%2F3%29%28y-1%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "compare to  <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;\" >   <BR>\n" );
document.write( "     \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p=28%2F3 ALIGN=MIDDLE  ALT=\"4p=28%2F3\"   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=28%2F12 ALIGN=MIDDLE  ALT=\"p=28%2F12\"   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=7%2F3 ALIGN=MIDDLE  ALT=\"p=7%2F3\"   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=h=2%2F3 ALIGN=MIDDLE  ALT=\"h=2%2F3\"   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%2F7 ALIGN=MIDDLE  ALT=\"k=1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so\r<BR>\n" );
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document.write( " vertex is 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;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F7 ALIGN=MIDDLE  ALT=\"+1%2F7\"   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=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%2Bp ALIGN=MIDDLE  ALT=\"+k%2Bp\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7%2B7%2F3 ALIGN=MIDDLE  ALT=\"1%2F7%2B7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52%2F21 ALIGN=MIDDLE  ALT=\"52%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "directrix: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=k-p=1%2F7-7%2F3=+-46%2F21 ALIGN=MIDDLE  ALT=\"y+=k-p=1%2F7-7%2F3=+-46%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "axis of symmetry: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=h ALIGN=MIDDLE  ALT=\"x=h\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2F3 ALIGN=MIDDLE  ALT=\"x=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "latus rectum:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p=+28%2F3 ALIGN=MIDDLE  ALT=\"4p=+28%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " endpoints of latus rectum: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2B2p ALIGN=MIDDLE  ALT=\"h%2B2p\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%2Bp ALIGN=MIDDLE  ALT=\"+k%2Bp\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h-2p ALIGN=MIDDLE  ALT=\"h-2p\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%2Bp ALIGN=MIDDLE  ALT=\"+k%2Bp\"   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=h%2B2p ALIGN=MIDDLE  ALT=\"h%2B2p\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2Bp ALIGN=MIDDLE  ALT=\"k%2Bp\"   DISABLED_style= \"max-width:90%; height:auto;\" >) =(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3%2B2%287%2F3%29 ALIGN=MIDDLE  ALT=\"2%2F3%2B2%287%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7%2B7%2F3 ALIGN=MIDDLE  ALT=\"1%2F7%2B7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F3 ALIGN=MIDDLE  ALT=\"16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52%2F21 ALIGN=MIDDLE  ALT=\"52%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "and <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h-2p ALIGN=MIDDLE  ALT=\"h-2p\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%2Bp ALIGN=MIDDLE  ALT=\"+k%2Bp\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3-2%287%2F3%29 ALIGN=MIDDLE  ALT=\"2%2F3-2%287%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F7%2B7%2F3 ALIGN=MIDDLE  ALT=\"+1%2F7%2B7%2F3\"   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=52%2F21 ALIGN=MIDDLE  ALT=\"52%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );