document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90260>Question 90260</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534494498/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the maximum value of y=x squared+6x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65542 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=65542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Are you sure it's not the minimum? No maximum occurs on the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B6x ALIGN=MIDDLE  ALT=\"y=x%5E2%2B6x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Well here's the solution to find the minimum\r<BR>\n" );
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document.write( "The minimum value occurs at the vertex of the graph\r<BR>\n" );
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document.write( "First determine the x-value of the vertex:\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;\" > Here is the general formula to find the x-value of the vertex\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%2B6x ALIGN=MIDDLE  ALT=\"y=x%5E2%2B6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that a=1 and b=6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-6%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=%28-6%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=6 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=%28-6%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-6%29%2F2\"   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=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\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=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   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%28-3%29 ALIGN=MIDDLE  ALT=\"f%28-3%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%2B6x ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B6x\"   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%28-3%29=%28-3%29%5E2%2B6%28-3%29 ALIGN=MIDDLE  ALT=\"f%28-3%29=%28-3%29%5E2%2B6%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   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%28-3%29=%289%29%2B6%28-3%29 ALIGN=MIDDLE  ALT=\"f%28-3%29=%289%29%2B6%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise -3 to the second power to get 9\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=%289%29%2B-18 ALIGN=MIDDLE  ALT=\"f%28-3%29=%289%29%2B-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 6 by -3 to get -18\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=-9 ALIGN=MIDDLE  ALT=\"f%28-3%29=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the vertex is (-3,-9)\r<BR>\n" );
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document.write( "So the minimum value is -9\r<BR>\n" );
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document.write( "If we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B6x ALIGN=MIDDLE  ALT=\"y=x%5E2%2B6x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can clearly see the minimum value\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-13%2C7%2C-19%2C1%2C%0D%0Agrid%28+1+%29%2C%0D%0Agraph%28900%2C900%2C-13%2C7%2C-19%2C1%2C+x%5E2%2B6x%29%2C%0D%0A%0D%0Acircle%28-3%2C-9%2C0.05%29%2C%0D%0Acircle%28-3%2C-9%2C0.08%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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