document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109226>Question 109226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi- this is my problem, that I need help with. State the maxium or minimum value of each quadratic function and name the x-value at which this occurs.<BR>\n" );
document.write( "f(x)= -2x^2-6x+5<BR>\n" );
document.write( "I don't know where to start, sorry!!!<BR>\n" );
document.write( "Thank you in advance for you help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #79641 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=79641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the x value at the min/max, 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%5E2-6x%2B5 ALIGN=MIDDLE  ALT=\"y=-2x%5E2-6x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that a=-2 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%2A-2%29 ALIGN=MIDDLE  ALT=\"x=%28--6%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in b=-6 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=6%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x=6%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -6 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=%286%29%2F-4 ALIGN=MIDDLE  ALT=\"x=%286%29%2F-4\"   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=-3%2F2 ALIGN=MIDDLE  ALT=\"x=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the min/max occurs at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F2 ALIGN=MIDDLE  ALT=\"x=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.5 ALIGN=MIDDLE  ALT=\"x=-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > in decimal form). Lets plug this into the equation to find the min/max\r<BR>\n" );
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document.write( "Lets evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1.5%29 ALIGN=MIDDLE  ALT=\"f%28-1.5%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%5E2-6x%2B5 ALIGN=MIDDLE  ALT=\"f%28x%29=-2x%5E2-6x%2B5\"   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%28-1.5%29=-2%28-1.5%29%5E2-6%28-1.5%29%2B5 ALIGN=MIDDLE  ALT=\"f%28-1.5%29=-2%28-1.5%29%5E2-6%28-1.5%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.5 ALIGN=MIDDLE  ALT=\"x=-1.5\"   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%28-1.5%29=-2%282.25%29-6%28-1.5%29%2B5 ALIGN=MIDDLE  ALT=\"f%28-1.5%29=-2%282.25%29-6%28-1.5%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise -1.5 to the second power to get 2.25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1.5%29=-4.5-6%28-1.5%29%2B5 ALIGN=MIDDLE  ALT=\"f%28-1.5%29=-4.5-6%28-1.5%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 by 2.25 to get 4.5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1.5%29=-4.5--9%2B5 ALIGN=MIDDLE  ALT=\"f%28-1.5%29=-4.5--9%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 6 by -1.5 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%28-1.5%29=-4.5%2B9%2B5 ALIGN=MIDDLE  ALT=\"f%28-1.5%29=-4.5%2B9%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate any negatives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1.5%29=9.5 ALIGN=MIDDLE  ALT=\"f%28-1.5%29=9.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So the min/max is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9.5 ALIGN=MIDDLE  ALT=\"y=9.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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%5E2-6x%2B5 ALIGN=MIDDLE  ALT=\"y=-2x%5E2-6x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > you 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-11.5%2C8.5%2C-0.5%2C19.5%2C%0D%0Agrid%28+1+%29%2C%0D%0Agraph%28900%2C900%2C-11.5%2C8.5%2C-0.5%2C19.5%2C+-2x%5E2-6x%2B5%29%2C%0D%0A%0D%0Acircle%28-1.5%2C9.5%2C0.05%29%2C%0D%0Acircle%28-1.5%2C9.5%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 you can see that the maximum <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9.5 ALIGN=MIDDLE  ALT=\"y=9.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > occurs at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.5 ALIGN=MIDDLE  ALT=\"x=-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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