document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=131896>Question 131896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the x and y coordinates of the vertex <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-2x%5E2%2B2x%2B6 ALIGN=MIDDLE  ALT=\"f%28x%29=-2x%5E2%2B2x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96299 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=96299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the x-coordinate of the vertex, we can use this formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-2x%5E2%2B2x%2B6 ALIGN=MIDDLE  ALT=\"f%28x%29=-2x%5E2%2B2x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that a=-2 and b=2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x=%28-2%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=2 and a=-2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%29%2F-4 ALIGN=MIDDLE  ALT=\"x=%28-2%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -2 to get -4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the  x-coordinate of the vertex is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "This also means that the line of symmetry is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now lets plug this into the equation to find the y-coordinate of the vertex.\r<BR>\n" );
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document.write( "Lets evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2F2%29 ALIGN=MIDDLE  ALT=\"f%281%2F2%29\"   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=f%28x%29=-2x%5E2%2B2x%2B6 ALIGN=MIDDLE  ALT=\"f%28x%29=-2x%5E2%2B2x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given polynomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2F2%29=-2%281%2F2%29%5E2%2B2%281%2F2%29%2B6 ALIGN=MIDDLE  ALT=\"f%281%2F2%29=-2%281%2F2%29%5E2%2B2%281%2F2%29%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   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=f%281%2F2%29=-2%281%2F4%29%2B2%281%2F2%29%2B6 ALIGN=MIDDLE  ALT=\"f%281%2F2%29=-2%281%2F4%29%2B2%281%2F2%29%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2F2%29=-1%2F2%2B2%281%2F2%29%2B6 ALIGN=MIDDLE  ALT=\"f%281%2F2%29=-1%2F2%2B2%281%2F2%29%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -2 by <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%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   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=f%281%2F2%29=-1%2F2%2B1%2B6 ALIGN=MIDDLE  ALT=\"f%281%2F2%29=-1%2F2%2B1%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 by <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 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2F2%29=13%2F2 ALIGN=MIDDLE  ALT=\"f%281%2F2%29=13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "So the vertex is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{1}{2},\frac{13}{2}\right)\">\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "This means that the x-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{2}\"> and the y-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{13}{2}\"><BR>\n" );
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