document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109691>Question 109691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the vertex of the parobola f(x)=-4x^2+40x-93 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #79954 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=79954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the vertex, we need to know 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=-4x%5E2%2B40x-93 ALIGN=MIDDLE  ALT=\"y=-4x%5E2%2B40x-93\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that a=-4 and b=40\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-40%29%2F%282%2A-4%29 ALIGN=MIDDLE  ALT=\"x=%28-40%29%2F%282%2A-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=40 and a=-4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-40%29%2F-8 ALIGN=MIDDLE  ALT=\"x=%28-40%29%2F-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -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=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   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=5 ALIGN=MIDDLE  ALT=\"x=5\"   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=5 ALIGN=MIDDLE  ALT=\"x=5\"   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%285%29 ALIGN=MIDDLE  ALT=\"f%285%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=-4x%5E2%2B40x-93 ALIGN=MIDDLE  ALT=\"f%28x%29=-4x%5E2%2B40x-93\"   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%285%29=-4%285%29%5E2%2B40%285%29-93 ALIGN=MIDDLE  ALT=\"f%285%29=-4%285%29%5E2%2B40%285%29-93\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   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%285%29=-4%2825%29%2B40%285%29-93 ALIGN=MIDDLE  ALT=\"f%285%29=-4%2825%29%2B40%285%29-93\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 5 to the second power to get 25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=-100%2B40%285%29-93 ALIGN=MIDDLE  ALT=\"f%285%29=-100%2B40%285%29-93\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 4 by 25 to get 100\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=-100%2B200-93 ALIGN=MIDDLE  ALT=\"f%285%29=-100%2B200-93\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 40 by 5 to get 200\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=7 ALIGN=MIDDLE  ALT=\"f%285%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the vertex is (5,7)\r<BR>\n" );
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document.write( "Notice if we graph the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4x%5E2%2B40x-93 ALIGN=MIDDLE  ALT=\"y=-4x%5E2%2B40x-93\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get\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-5%2C15%2C-3%2C17%2C%0D%0Agrid%28+1+%29%2C%0D%0Agraph%28900%2C900%2C-5%2C15%2C-3%2C17%2C+-4x%5E2%2B40x-93%29%2C%0D%0Acircle%283%2C-9%2C0.05%29%2C%0D%0Acircle%283%2C-9%2C0.08%29%2C%0D%0Acircle%284%2C3%2C0.05%29%2C%0D%0Acircle%284%2C3%2C0.08%29%2C%0D%0Acircle%285%2C7%2C0.05%29%2C%0D%0Acircle%285%2C7%2C0.08%29%2C%0D%0Acircle%286%2C3%2C0.05%29%2C%0D%0Acircle%286%2C3%2C0.08%29%2C%0D%0Acircle%287%2C-9%2C0.05%29%2C%0D%0Acircle%287%2C-9%2C0.08%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and we can see that the vertex is (5,7)<BR>\n" );
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