document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=948181>Question 948181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a hard time solving this. Can you help?\r<BR>\n" );
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document.write( "The profit function for selling x units of a certain product is given by <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-x%5E2%2B900x-160%2C000 ALIGN=MIDDLE  ALT=\"P%28x%29=-x%5E2%2B900x-160%2C000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A.)State the value of 'a', 'b,' and 'c' of the quadratic function P(x).<BR>\n" );
document.write( "B.)Find the vertex of the graph of P(x).<BR>\n" );
document.write( "C.)For what number of units is maximum profit achieved?<BR>\n" );
document.write( "   What is the maximum profit? Remember to include appropriate labels (units) in your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578682 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=578682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The comma interferes with the rendering.  Your function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-x%5E2%2B900x-160000 ALIGN=MIDDLE  ALT=\"P%28x%29=-x%5E2%2B900x-160000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(A):\r<BR>\n" );
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document.write( "P is given in general form so just read the values from the function definition as given.\r<BR>\n" );
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document.write( "(B) & (C):\r<BR>\n" );
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document.write( "You can put into standard form using completion of the square, but here is using the roots<BR>\n" );
document.write( "and getting the midpoint value between them:\r<BR>\n" );
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document.write( "Roots of P, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-900%2F%28%282%29%28-1%29%29%2B-+sqrt%28810000-4%28-1%29%28-160000%29%29%2F%282%28-1%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Omitting the arithmetic simplification steps, your will find the roots to be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28450%2B-+50sqrt%2817%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28450%2B-+50sqrt%2817%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, what is the exact middle of those roots?<BR>\n" );
document.write( "Find their sum, divide by 2, and find ...<BR>\n" );
document.write( "that the axis of symmetry for P is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=450 ALIGN=MIDDLE  ALT=\"x=450\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<b>EVALUATE P at x=450.</b><BR>\n" );
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