document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153056>Question 1153056</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The profits of Mr. Unlucky’s company can be represented by the equation p(x)=-3x^2+18x-4 where p(x) is the amount of profit in hundreds of thousands of dollars and x is the number of years of operation. He realizes his company is on the downturn and wishes to sell before he ends up in debt.\r<BR>\n" );
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document.write( "a. When will Mr. Unlucky’s business show the maximum profit? ___  years\r<BR>\n" );
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document.write( "b. What is the maximum profit? ____ hundreds of thousands\r<BR>\n" );
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document.write( "c. During what time period will Mr. Unlucky expect his business’ profits to be on the downturn? After ___  years </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775207 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=775207\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=-3x%5E2%2B18x-4 ALIGN=MIDDLE  ALT=\"p%28x%29=-3x%5E2%2B18x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29 ALIGN=MIDDLE  ALT=\"p%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the amount of profit in hundreds of thousands of dollars and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the number of years of operation. <BR>\n" );
document.write( "He realizes his company is on the downturn and wishes to sell before he ends up in debt.\r<BR>\n" );
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document.write( "a. When will Mr. Unlucky’s business show the maximum profit? ___ years\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=-3x%5E2%2B18x-4 ALIGN=MIDDLE  ALT=\"p%28x%29=-3x%5E2%2B18x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...since you have an upside down parabola, max is at vertex; so, write your 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=p%28x%29=-3x%5E2%2B18x-4 ALIGN=MIDDLE  ALT=\"p%28x%29=-3x%5E2%2B18x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >....group <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E2%2B18x ALIGN=MIDDLE  ALT=\"-3x%5E2%2B18x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-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=p%28x%29=-3%28x%5E2-6x%29-4 ALIGN=MIDDLE  ALT=\"p%28x%29=-3%28x%5E2-6x%29-4\"   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=p%28x%29=-3%28x%5E2-6x%2Bb%5E2%29-%28-3%29b%5E2-4 ALIGN=MIDDLE  ALT=\"p%28x%29=-3%28x%5E2-6x%2Bb%5E2%29-%28-3%29b%5E2-4\"   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=p%28x%29=-3%28x%5E2-6x%2B3%5E2%29%2B3%2A3%5E2-4 ALIGN=MIDDLE  ALT=\"p%28x%29=-3%28x%5E2-6x%2B3%5E2%29%2B3%2A3%5E2-4\"   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=p%28x%29=-3%28x-3%29%5E2%2B27-4 ALIGN=MIDDLE  ALT=\"p%28x%29=-3%28x-3%29%5E2%2B27-4\"   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=p%28x%29=-3%28x-3%29%5E2%2B23 ALIGN=MIDDLE  ALT=\"p%28x%29=-3%28x-3%29%5E2%2B23\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3 ALIGN=MIDDLE  ALT=\"h=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=23 ALIGN=MIDDLE  ALT=\"k=23\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " the maximum profit is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > years\r<BR>\n" );
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document.write( "b. What is the maximum profit? ____ hundreds of thousands\r<BR>\n" );
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document.write( "the maximum profit is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23 ALIGN=MIDDLE  ALT=\"23\"   DISABLED_style= \"max-width:90%; height:auto;\" > hundreds of thousands\r<BR>\n" );
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document.write( "c. During what time period will Mr. Unlucky expect his business’ profits to be on the downturn? After <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > years\r<BR>\n" );
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document.write( " </SPAN>\n" );
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