document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=131104>Question 131104</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=3x%5E2-24x%2B51 ALIGN=MIDDLE  ALT=\"f%28x%29=3x%5E2-24x%2B51\"   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 #95727 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=95727\">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=3x%5E2-24x%2B51 ALIGN=MIDDLE  ALT=\"y=3x%5E2-24x%2B51\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that a=3 and b=-24\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28--24%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x=%28--24%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=-24 and a=3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=24%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x=24%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -24 to get 24\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2824%29%2F6 ALIGN=MIDDLE  ALT=\"x=%2824%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 3 to get 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   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=4 ALIGN=MIDDLE  ALT=\"x=4\"   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=4 ALIGN=MIDDLE  ALT=\"x=4\"   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%284%29 ALIGN=MIDDLE  ALT=\"f%284%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=3x%5E2-24x%2B51 ALIGN=MIDDLE  ALT=\"f%28x%29=3x%5E2-24x%2B51\"   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%284%29=3%284%29%5E2-24%284%29%2B51 ALIGN=MIDDLE  ALT=\"f%284%29=3%284%29%5E2-24%284%29%2B51\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   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%284%29=3%2816%29-24%284%29%2B51 ALIGN=MIDDLE  ALT=\"f%284%29=3%2816%29-24%284%29%2B51\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 4 to the second power 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%284%29=48-24%284%29%2B51 ALIGN=MIDDLE  ALT=\"f%284%29=48-24%284%29%2B51\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 3 by 16 to get 48\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%29=48-96%2B51 ALIGN=MIDDLE  ALT=\"f%284%29=48-96%2B51\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 24 by 4 to get 96\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%29=3 ALIGN=MIDDLE  ALT=\"f%284%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the vertex is (4,3)\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=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the vertex is (4,3)\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+3x%5E2-24x%2B51%29%2C%0D%0Aline%284%2C-12%2C4%2C12%29%2C%0D%0Acircle%284%2C3%2C0.05%29%2C%0D%0Acircle%284%2C3%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=3x%5E2-24x%2B51 ALIGN=MIDDLE  ALT=\"f%28x%29=3x%5E2-24x%2B51\"   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=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the vertex (4,3) </SPAN>\n" );
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