document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=750980>Question 750980</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you complete the square to put in the form f(x)= a(x-h)^2 +k\r<BR>\n" );
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document.write( "f(x)=-x^2+4x-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456941 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39625)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=456941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You would add a term and subtract the same term, allowing you to convert part of the expression into a factorable square trinomial.  Your given function would be handled this way:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B4x-5=-1%2A%28x%5E2-4x%2B5%29 ALIGN=MIDDLE  ALT=\"-x%5E2%2B4x-5=-1%2A%28x%5E2-4x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, factor a -1\r<BR>\n" );
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document.write( "See the non-square part which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x ALIGN=MIDDLE  ALT=\"x%5E2-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which can be factored into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-4%29 ALIGN=MIDDLE  ALT=\"x%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is like a representation of a rectangle of x by (x-4) area.  You could imagine cutting the longer length  to leave a square area, cut the extra piece in half and put one of them along the other neighboring side of the square piece.  A drawing would be better, as would be found in a few intermediate algebra books.  Anyway, you will notice a missing square corner.  THAT represents the term to both add and subtract symbolically.\r<BR>\n" );
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document.write( "Continuing....\r<BR>\n" );
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document.write( "You want <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2F2%29%5E2=4 ALIGN=MIDDLE  ALT=\"%28-4%2F2%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is that missing square term.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A%28x%5E2-4x%2B5%29=-1%2A%28x%5E2-4x%2B4%2B5-4%29 ALIGN=MIDDLE  ALT=\"-1%2A%28x%5E2-4x%2B5%29=-1%2A%28x%5E2-4x%2B4%2B5-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A%28%28x-2%29%5E2%2B5-4%29 ALIGN=MIDDLE  ALT=\"-1%2A%28%28x-2%29%5E2%2B5-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A%28%28x-2%29%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"-1%2A%28%28x-2%29%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A%28x-2%29%5E2-1 ALIGN=MIDDLE  ALT=\"-1%2A%28x-2%29%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, square completed.\r<BR>\n" );
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document.write( "The standard form for your function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28x%29=-1%28x-2%29%5E2-1%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28x%29=-1%28x-2%29%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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