document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133084>Question 133084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you determine the min or max of -3x^2+24x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97298 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=97298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the min/max of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E2%2B24x ALIGN=MIDDLE  ALT=\"-3x%5E2%2B24x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need to find the vertex. However, we first need to find the axis of symmetry\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=-3x%5E2%2B24x ALIGN=MIDDLE  ALT=\"y=-3x%5E2%2B24x\"   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%2A-3%29 ALIGN=MIDDLE  ALT=\"x=%28-24%29%2F%282%2A-3%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=%28-24%29%2F-6 ALIGN=MIDDLE  ALT=\"x=%28-24%29%2F-6\"   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 axis 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%2B24x ALIGN=MIDDLE  ALT=\"f%28x%29=-3x%5E2%2B24x\"   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%2B24%284%29 ALIGN=MIDDLE  ALT=\"f%284%29=-3%284%29%5E2%2B24%284%29\"   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%2B24%284%29 ALIGN=MIDDLE  ALT=\"f%284%29=-3%2816%29%2B24%284%29\"   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%2B24%284%29 ALIGN=MIDDLE  ALT=\"f%284%29=-48%2B24%284%29\"   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%2B96 ALIGN=MIDDLE  ALT=\"f%284%29=-48%2B96\"   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=48 ALIGN=MIDDLE  ALT=\"f%284%29=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the vertex is (4,48)\r<BR>\n" );
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document.write( "Now since the leading coefficient is -3, this means that the parabola opens down. So at the vertex there is a maximum. Also, this means that the max is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=48 ALIGN=MIDDLE  ALT=\"y=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > which occurs at <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;\" > </SPAN>\n" );
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