document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182599>Question 1182599</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following equation models the rate at which a worker produces so many units after x hours when the worker starts at 8AM. (Assume 8AM means x=0) <BR>\n" );
document.write( "f(x)=-2x^2+8x+50\r<BR>\n" );
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document.write( "At what time is the worker working most efficiently and how many units is the worker producing at this time? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812674 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812674\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The following equation models the rate at which a worker produces so many units after x hours when the worker starts at 8AM (Assume 8AM means x=0)\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%2B8x%2B50 ALIGN=MIDDLE  ALT=\"f%28x%29=-2x%5E2%2B8x%2B50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "At what time is the worker working most efficiently and how many units is the worker producing at this time?\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%2B8x%2B50 ALIGN=MIDDLE  ALT=\"f%28x%29=-2x%5E2%2B8x%2B50\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> this is downward parabola and max is at vertex\r<BR>\n" );
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document.write( "so, write equation in vertex form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28-2x%5E2%2B8x%29%2B50 ALIGN=MIDDLE  ALT=\"f%28x%29=%28-2x%5E2%2B8x%29%2B50\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   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=-2%28x%5E2-4x%29%2B50 ALIGN=MIDDLE  ALT=\"f%28x%29=-2%28x%5E2-4x%29%2B50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......complete square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-2%28x%5E2-4x%2Bb%5E2%29-%28-2%29b%5E2%2B50 ALIGN=MIDDLE  ALT=\"f%28x%29=-2%28x%5E2-4x%2Bb%5E2%29-%28-2%29b%5E2%2B50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4%2F2=2 ALIGN=MIDDLE  ALT=\"b=4%2F2=2\"   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=-2%28x%5E2-4x%2B2%5E2%29%2B2%2A2%5E2%2B50 ALIGN=MIDDLE  ALT=\"f%28x%29=-2%28x%5E2-4x%2B2%5E2%29%2B2%2A2%5E2%2B50\"   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=-2%28x-2%29%5E2%2B8%2B50 ALIGN=MIDDLE  ALT=\"f%28x%29=-2%28x-2%29%5E2%2B8%2B50\"   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=-2%28x-2%29%5E2%2B58 ALIGN=MIDDLE  ALT=\"f%28x%29=-2%28x-2%29%5E2%2B58\"   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=h=2 ALIGN=MIDDLE  ALT=\"h=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=58 ALIGN=MIDDLE  ALT=\"k=58\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> vertex is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=58 ALIGN=MIDDLE  ALT=\"58\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Assuming <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8AM ALIGN=MIDDLE  ALT=\"8AM\"   DISABLED_style= \"max-width:90%; height:auto;\" > means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10AM ALIGN=MIDDLE  ALT=\"10AM\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the worker working most efficiently at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10AM ALIGN=MIDDLE  ALT=\"10AM\"   DISABLED_style= \"max-width:90%; height:auto;\" >   and producing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=58 ALIGN=MIDDLE  ALT=\"58\"   DISABLED_style= \"max-width:90%; height:auto;\" > units at this time \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+600%2C+600%2C+-10%2C10%2C+-10%2C+65%2C+circle%282%2C58%2C.15%29%2Clocate%282%2C58%2Cv%282%2C58%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+65%2C+-2%28x-2%29%5E2%2B58%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );