document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203027>Question 1203027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The effectiveness of a television commercial depends on how many times a viewer watches it.After some experiments, an advertising agency found that if the effectiveness E is measured on a scale of 0 to 10,then E(n)=2/3×n-1/90×n^2, where n is the number of times a viewer watches a given commercial .By completing the square of E(n),find how many times a viewer should watch the commercial for a commercial to have maximum effectiveness? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838245 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=838245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given that\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++E%28n%29=%282%2F3%29n-%281%2F90%29n%5E2 ALIGN=MIDDLE  ALT=\"++E%28n%29=%282%2F3%29n-%281%2F90%29n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "measured on a scale of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0 ALIGN=MIDDLE  ALT=\"+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10 ALIGN=MIDDLE  ALT=\"+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The maximum vale of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+E ALIGN=MIDDLE  ALT=\"+E\"   DISABLED_style= \"max-width:90%; height:auto;\" > is occurs  when\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++dE%2Fdn+=+0 ALIGN=MIDDLE  ALT=\"++dE%2Fdn+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++E%28n%29=%282%2F3%29n-%281%2F90%29n%5E2 ALIGN=MIDDLE  ALT=\"++E%28n%29=%282%2F3%29n-%281%2F90%29n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++dE%2Fdn+=+2%2F+3+-2%281%2F90%29n ALIGN=MIDDLE  ALT=\"++dE%2Fdn+=+2%2F+3+-2%281%2F90%29n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For maximum\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F+3+-2%281%2F90%29n+=+0 ALIGN=MIDDLE  ALT=\"+2%2F+3+-2%281%2F90%29n+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F3+-+n%2F45+=+0 ALIGN=MIDDLE  ALT=\"+2%2F3+-+n%2F45+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2830+-+n%29%2F45+=+0 ALIGN=MIDDLE  ALT=\"+%2830+-+n%29%2F45+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=30 ALIGN=MIDDLE  ALT=\"+n+=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "OR, you can find a vertex if you write given equation in vertex form\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+E%28n%29=%282%2F3%29n-%281%2F90%29n%5E2 ALIGN=MIDDLE  ALT=\"+E%28n%29=%282%2F3%29n-%281%2F90%29n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >......complete square\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+E%28n%29=10+-+1%2F90+%28n+-+30%29%5E2 ALIGN=MIDDLE  ALT=\"+E%28n%29=10+-+1%2F90+%28n+-+30%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n=30 ALIGN=MIDDLE  ALT=\"+n=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=30 ALIGN=MIDDLE  ALT=\"+n+=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+600%2C+600%2C+-6%2C+60%2C+-60%2C+60%2C+circle%2830%2C10%2C.5%29%2C%0D%0Agraph%28+600%2C+600%2C+-6%2C+60%2C+-60%2C+60%2C+%282%2F3%29x-%281%2F90%29x%5E2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );