document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112191>Question 112191</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write y=2x^2+12x+14 in vertex form </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81840 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=81840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2%2B12x%2B14 ALIGN=MIDDLE  ALT=\"y=2x%5E2%2B12x%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-14=2x%5E2%2B12x ALIGN=MIDDLE  ALT=\"y-14=2x%5E2%2B12x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14++ ALIGN=MIDDLE  ALT=\"14++\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-14=2%2A%28x%5E2%2B6%2Ax%29 ALIGN=MIDDLE  ALT=\"y-14=2%2A%28x%5E2%2B6%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the leading coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2++ ALIGN=MIDDLE  ALT=\"2++\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This step is important since we want the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient to be 1.  \r<BR>\n" );
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document.write( "Take half of the x coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F2=3 ALIGN=MIDDLE  ALT=\"6%2F2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Now square  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29%5E2=9 ALIGN=MIDDLE  ALT=\"%283%29%5E2=9\"   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=y-14=2%2A%28x%5E2%2B6%2Ax%2B9%29 ALIGN=MIDDLE  ALT=\"y-14=2%2A%28x%5E2%2B6%2Ax%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add this number (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >) to the expression inside the parenthesis. Now the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6%2Ax%2B9 ALIGN=MIDDLE  ALT=\"x%5E2%2B6%2Ax%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a perfect square trinomial.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-14%2B%282%29%289%29=2%2A%28x%5E2%2B6%2Ax%2B9%29 ALIGN=MIDDLE  ALT=\"y-14%2B%282%29%289%29=2%2A%28x%5E2%2B6%2Ax%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since we added <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > inside the parenthesis, we need to add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%289%29 ALIGN=MIDDLE  ALT=\"%282%29%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the other side (remember, we factored out the leading coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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=y-14%2B%282%29%289%29=2%2A%28x%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"y-14%2B%282%29%289%29=2%2A%28x%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6%2Ax%2B9 ALIGN=MIDDLE  ALT=\"x%5E2%2B6%2Ax%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now the right side is a perfect square  (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4=2%2A%28x%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"y%2B4=2%2A%28x%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   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=y=2%2A%28x%2B3%29%5E2-4 ALIGN=MIDDLE  ALT=\"y=2%2A%28x%2B3%29%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4 from both sides\r<BR>\n" );
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document.write( "Now the equation is in vertex form\r<BR>\n" );
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