document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=666161>Question 666161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Put in vertex form: <BR>\n" );
document.write( "  f(x)= -2x^2 +4x -6 \r<BR>\n" );
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document.write( "\"^2\", means squared. \r<BR>\n" );
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document.write( "Thank you SOO much for your time!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #414308 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=414308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To clarify, the equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-2x%5E2%2B4x-6 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-2x%5E2%2B4x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "One way to put this in vertex form is to complete the square.\r<BR>\n" );
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document.write( "-2x^2 +4x = 6\r<BR>\n" );
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document.write( "One pre-requisite of completing the square is to have the coefficient of the squared term to be 1. So factor out a -2.\r<BR>\n" );
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document.write( "-2(x^2-2x) = 6\r<BR>\n" );
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document.write( "-2(x^2-2x+1) = 6+-2(1) (completing the square step since (-2/2)^2 = 1\r<BR>\n" );
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document.write( "-2(x-1)^2 = 4 (since x^2-2x+1 is (x-1)^2)\r<BR>\n" );
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document.write( "-2(x-1)^2 - 4 is our vertex form.\r<BR>\n" );
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document.write( "Notice this satisfies our a(x-h)^2 + k form.\r<BR>\n" );
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document.write( "To check:\r<BR>\n" );
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document.write( "In general for ax^2+bx+c where our vertex is (h,k), we have that\r<BR>\n" );
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document.write( "a = -2\r<BR>\n" );
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document.write( "h = -b/2a = -4 / -4 = 1<BR>\n" );
document.write( "k = f(h) = f(1) =  -2+4-6 = -4\r<BR>\n" );
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document.write( "So our a(x-h)^2 +k could have been done in this fashion since a = -2, h = 1, k = -4 hence -2(x-1)^2 -4\r<BR>\n" );
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document.write( " </SPAN>\n" );
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