document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=946390>Question 946390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am given the equation f(x)=300x-11x squared +2. I am asked to find the maximum. Normally the homework problems show step by step instruction although this one isn't. Can you please help we with this </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #577356 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=577356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your function is f(x)=300x-11x^2+2, restatable as f(x)=-11x^2+300x+2.<BR>\n" );
document.write( "Adding the proper rendering tags, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-11x%5E2%2B300x%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29=-11x%5E2%2B300x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The function f is a parabola opening downward, therefore having a maximum.  If f has real<BR>\n" );
document.write( "roots, they can be used for finding the symmetry axis, and from it, the maximum of f.\r<BR>\n" );
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document.write( "Not clear which method you are allowed here.  One way is, complete the square to put into<BR>\n" );
document.write( "standard form.  The other way is, find the roots of f, find the midpoint of those roots, and<BR>\n" );
document.write( "use that value to find corresponding f.\r<BR>\n" );
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document.write( "I will start this using Completing The Square, which might possibly not be the easiest way.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11x%5E2%2B300x%2B2 ALIGN=MIDDLE  ALT=\"-11x%5E2%2B300x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%28x%5E2-%28300%2F11%29x-2%2F11%29 ALIGN=MIDDLE  ALT=\"-11%28x%5E2-%28300%2F11%29x-2%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%28x%5E2-%28300%2F11%29x%2B%28150%2F11%29%5E2-2%2F11-%28150%2F11%29%5E2%29 ALIGN=MIDDLE  ALT=\"-11%28x%5E2-%28300%2F11%29x%2B%28150%2F11%29%5E2-2%2F11-%28150%2F11%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%28%28x-150%2F11%29%5E2-2%2F11-%28150%2F11%29%5E2%29 ALIGN=MIDDLE  ALT=\"-11%28%28x-150%2F11%29%5E2-2%2F11-%28150%2F11%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%28%28x-150%2F11%29%5E2-22%2F11%5E2-150%5E2%2F11%5E2%29 ALIGN=MIDDLE  ALT=\"-11%28%28x-150%2F11%29%5E2-22%2F11%5E2-150%5E2%2F11%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%28%28x-150%29%5E2-%2822%2B150%5E2%29%2F11%5E2%29 ALIGN=MIDDLE  ALT=\"-11%28%28x-150%29%5E2-%2822%2B150%5E2%29%2F11%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now distrubute the previously factored Negative Eleven.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28-11%28x-150%29%5E2%2B%2822%2B150%5E2%29%2F11%29 ALIGN=MIDDLE  ALT=\"highlight%28-11%28x-150%29%5E2%2B%2822%2B150%5E2%29%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the equivalent form of your function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28x%29=-11%28x-150%29%5E2%2B%2822%2B150%5E2%29%2F11%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28x%29=-11%28x-150%29%5E2%2B%2822%2B150%5E2%29%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and I have simply not finished the computation for the constant term.  The vertex for the<BR>\n" );
document.write( "maximum point is  at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=150%29 ALIGN=MIDDLE  ALT=\"highlight%28x=150%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28y=%2822%2B150%5E2%29%2F11%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28y=%2822%2B150%5E2%29%2F11%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  this being the maximum value.\r<BR>\n" );
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document.write( "You may need to study or review how to Complete The Square, and also about Standard Form for a parabola. </SPAN>\n" );
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