document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113934>Question 113934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the vertex of the parabola defined by y = 2x(squared)+8x+9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82913 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=82913\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the vertex, we first need to find the axis of symmetry (ie the x-coordinate of the vertex)\r<BR>\n" );
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document.write( "To find the axis 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=2x%5E2%2B8x%2B9 ALIGN=MIDDLE  ALT=\"y=2x%5E2%2B8x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that a=2 and b=8\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-8%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x=%28-8%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=8 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=%28-8%29%2F4 ALIGN=MIDDLE  ALT=\"x=%28-8%29%2F4\"   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=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the axis of symmetry is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   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=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   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%28-2%29 ALIGN=MIDDLE  ALT=\"f%28-2%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%2B8x%2B9 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E2%2B8x%2B9\"   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%28-2%29=2%28-2%29%5E2%2B8%28-2%29%2B9 ALIGN=MIDDLE  ALT=\"f%28-2%29=2%28-2%29%5E2%2B8%28-2%29%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-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=f%28-2%29=2%284%29%2B8%28-2%29%2B9 ALIGN=MIDDLE  ALT=\"f%28-2%29=2%284%29%2B8%28-2%29%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise -2 to the second power to get 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=8%2B8%28-2%29%2B9 ALIGN=MIDDLE  ALT=\"f%28-2%29=8%2B8%28-2%29%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 by 4 to get 8\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=8%2B-16%2B9 ALIGN=MIDDLE  ALT=\"f%28-2%29=8%2B-16%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 8 by -2 to get -16\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=1 ALIGN=MIDDLE  ALT=\"f%28-2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the vertex is (-2,1)\r<BR>\n" );
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document.write( "Notice if you graph the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2%2B8x%2B9 ALIGN=MIDDLE  ALT=\"y=2x%5E2%2B8x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > you can see that the vertex is (-2,1). So this visually verifies 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-12%2C8%2C-9%2C11%2C%0D%0Agrid%28+1+%29%2C%0D%0Agraph%28900%2C900%2C-12%2C8%2C-9%2C11%2C+2x%5E2%2B8x%2B9%29%2C%0D%0Acircle%28-2%2C1%2C0.05%29%2C%0D%0Acircle%28-2%2C1%2C0.08%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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