document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=17561>Question 17561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you write in the form of y=a(x-p)2+q from y=x2-6x+10? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #8466 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=8466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the process called \"completing the square\".  Given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2+-+6x%2B10 ALIGN=MIDDLE  ALT=\"y=x%5E2+-+6x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" >  you need to write this in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+%28_____%29%5E2+%2B+___ ALIGN=MIDDLE  ALT=\"y=+%28_____%29%5E2+%2B+___\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You do this by taking the coefficient of x, which is -6, and take half of it, and square, which is +9.  The trick is to add +9 and subtract 9 on the right side, in order to do what needs to be done, but keep the equation the same.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+-6x+%2B9+-+9+%2B+10 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+-6x+%2B9+-+9+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice that the quantity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-6x%2B9+ ALIGN=MIDDLE  ALT=\"x%5E2+-6x%2B9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a perfect square trinomial, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+6x%2B9+=+%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+-+6x%2B9+=+%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, write:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%5E2+-6x+%2B9%29+-+9+%2B+10 ALIGN=MIDDLE  ALT=\"y+=+%28x%5E2+-6x+%2B9%29+-+9+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x-3%29%5E2+%2B1 ALIGN=MIDDLE  ALT=\"y+=+%28x-3%29%5E2+%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "That should do it!  In your formula, a=1, p=3 and q = 1.  Right??\r<BR>\n" );
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document.write( "Also, the vertex is at x=3 and y = 1, which is (p,q) = (3,1)!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph+%28300%2C300%2C+-10%2C10%2C-10%2C10%2C+x%5E2-6x%2B10%29 ALIGN=MIDDLE  ALT=\"+graph+%28300%2C300%2C+-10%2C10%2C-10%2C10%2C+x%5E2-6x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Is (3.1) the vertex of this parabola???\r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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