document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162179>Question 162179</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to write each function in vertex form, and identity it's vertex.\r<BR>\n" );
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document.write( "g(x)=x^2-1/2x+1\r<BR>\n" );
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document.write( "could you please guide me on the step by step process on how to work this.\r<BR>\n" );
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document.write( "please help soon!\r<BR>\n" );
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document.write( "thx :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119501 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=119501\">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=x%5E2-%281%2F2%29x%2B1 ALIGN=MIDDLE  ALT=\"x%5E2-%281%2F2%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "Take half of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F4 ALIGN=MIDDLE  ALT=\"-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28-1%2F2%29=-1%2F4 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28-1%2F2%29=-1%2F4\"   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=-1%2F4 ALIGN=MIDDLE  ALT=\"-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F16 ALIGN=MIDDLE  ALT=\"1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F4%29%5E2=%28-1%2F4%29%28-1%2F4%29=1%2F16 ALIGN=MIDDLE  ALT=\"%28-1%2F4%29%5E2=%28-1%2F4%29%28-1%2F4%29=1%2F16\"   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=x%5E2-%281%2F2%29x%2Bhighlight%281%2F16-1%2F16%29%2B1 ALIGN=MIDDLE  ALT=\"x%5E2-%281%2F2%29x%2Bhighlight%281%2F16-1%2F16%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add <font size=4><b>and</b></font> subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F16 ALIGN=MIDDLE  ALT=\"1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Make sure to place this after the \"x\" term. Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F16-1%2F16=0 ALIGN=MIDDLE  ALT=\"1%2F16-1%2F16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the expression is not changed.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-%281%2F2%29x%2B1%2F16%29-1%2F16%2B1 ALIGN=MIDDLE  ALT=\"%28x%5E2-%281%2F2%29x%2B1%2F16%29-1%2F16%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the first three terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%2F4%29%5E2-1%2F16%2B1 ALIGN=MIDDLE  ALT=\"%28x-1%2F4%29%5E2-1%2F16%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%281%2F2%29x%2B1%2F16 ALIGN=MIDDLE  ALT=\"x%5E2-%281%2F2%29x%2B1%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-+1%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-+1%2F4%29%5E2\"   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-1%2F4%29%5E2%2B15%2F16 ALIGN=MIDDLE  ALT=\"%28x-1%2F4%29%5E2%2B15%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So after completing the square, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%281%2F2%29x%2B1 ALIGN=MIDDLE  ALT=\"x%5E2-%281%2F2%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > transforms to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%2F4%29%5E2%2B15%2F16 ALIGN=MIDDLE  ALT=\"%28x-1%2F4%29%5E2%2B15%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-1%2F2x%2B1=%28x-1%2F4%29%5E2%2B15%2F16 ALIGN=MIDDLE  ALT=\"x%5E2-1%2F2x%2B1=%28x-1%2F4%29%5E2%2B15%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=x%5E2-%281%2F2%29x+%2B1 ALIGN=MIDDLE  ALT=\"g%28x%29=x%5E2-%281%2F2%29x+%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%28x-1%2F4%29%5E2%2B15%2F16 ALIGN=MIDDLE  ALT=\"g%28x%29=%28x-1%2F4%29%5E2%2B15%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%28x-1%2F4%29%5E2%2B15%2F16 ALIGN=MIDDLE  ALT=\"g%28x%29=%28x-1%2F4%29%5E2%2B15%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in vertex form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the vertex is (h,k)\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=1%2F4 ALIGN=MIDDLE  ALT=\"h=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=15%2F16 ALIGN=MIDDLE  ALT=\"k=15%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the vertex is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{1}{4},\frac{15}{16}\right)\"> </SPAN>\n" );
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