document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=131105>Question 131105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertex and the axis of symmetry for the following graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-x%5E2%2B2x%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E2%2B2x%2B3\"   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 #95728 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=95728\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the vertex, we first need to find the line of symmetry (ie the x-coordinate of the vertex)\r<BR>\n" );
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document.write( "To find the line of symmetry, 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=y=-x%5E2%2B2x%2B3 ALIGN=MIDDLE  ALT=\"y=-x%5E2%2B2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that a=-1 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-1%29 ALIGN=MIDDLE  ALT=\"x=%28-2%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=2 and a=-1\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-2 ALIGN=MIDDLE  ALT=\"x=%28-2%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -1 to get -2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the line of symmetry is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. 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%29 ALIGN=MIDDLE  ALT=\"f%281%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=-x%5E2%2B2x%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E2%2B2x%2B3\"   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%29=-%281%29%5E2%2B2%281%29%2B3 ALIGN=MIDDLE  ALT=\"f%281%29=-%281%29%5E2%2B2%281%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   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%29=-%281%29%2B2%281%29%2B3 ALIGN=MIDDLE  ALT=\"f%281%29=-%281%29%2B2%281%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 1 to the second power 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%29=-%281%29%2B2%2B3 ALIGN=MIDDLE  ALT=\"f%281%29=-%281%29%2B2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 by 1 to get 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=4 ALIGN=MIDDLE  ALT=\"f%281%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the vertex is (1,4)\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the line of symmetry is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the vertex is (1,4)\r<BR>\n" );
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document.write( "If we graph, we can visually verify our answer\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28900%2C900%2C-10%2C10%2C-10%2C10%2C%0D%0Agraph%28900%2C900%2C-10%2C10%2C-10%2C10%2C-x%5E2%2B2x%2B3%29%2C%0D%0Aline%281%2C-12%2C1%2C12%29%2C%0D%0Acircle%281%2C4%2C0.05%29%2C%0D%0Acircle%281%2C4%2C0.08%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-x%5E2%2B2x%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E2%2B2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the line of symmetry <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the vertex (1,4)<BR>\n" );
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