document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=383959>Question 383959</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello! I am needing help on a word problem.  \r<BR>\n" );
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document.write( "Macro Manufacturing estimates that its profit P in hundreds of dollars is P= -2x^2 + 20x-2 where x is the number of units produced in thousands.  How many units must be produced to obtain maximum profit?  \r<BR>\n" );
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document.write( "Thanks so much!  \r<BR>\n" );
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document.write( "Denise  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #271896 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=271896\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the max or min for a quadratic equation, convert to vertex form (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >) by completing the square.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=+-2x%5E2+%2B+20x-2 ALIGN=MIDDLE  ALT=\"P=+-2x%5E2+%2B+20x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=-2%28x%5E2-10x%29-2 ALIGN=MIDDLE  ALT=\"P=-2%28x%5E2-10x%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=-2%28x%5E2-10x%2B25%29-2%2B2%2825%29 ALIGN=MIDDLE  ALT=\"P=-2%28x%5E2-10x%2B25%29-2%2B2%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=-2%28x-5%29%5E2-2%2B50 ALIGN=MIDDLE  ALT=\"P=-2%28x-5%29%5E2-2%2B50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=-2%28x-5%29%5E2%2B48 ALIGN=MIDDLE  ALT=\"P=-2%28x-5%29%5E2%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The vertex is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" >), with a maximum profit of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" > hundred dollars which occurs when <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;\" > thousand units are produced.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C8%2C-5%2C55%2Cgrid%281%29%2Ccircle%285%2C48%2C0.25%29%2Cblue%28line%285%2C-100%2C5%2C100%29%29%2Cgraph%28300%2C300%2C-2%2C8%2C-5%2C55%2C0%2C-2%28x-5%29%5E2%2B48%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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