document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025991>Question 1025991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Between 1995 and 2010, the population of Smalltown, USA (in thousands) can modeled  by f(x)=-2x^2+30+17, where x=0 represents 1993. Based on this model, what was the maximum population? In what year did the population of Smalltown USA reach its maximum?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641264 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+-2x%5E2+%2B+30x+%2B+17+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+-2x%5E2+%2B+30x+%2B+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( Is this correct? )<BR>\n" );
document.write( "The formula for maximum is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+-30%2F%28+2%2A%28-2%29+%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+-30%2F%28+2%2A%28-2%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+15%2F2+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+15%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug this result back into formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28+15%2F2+%29+=+-2%2A%28+15%2F2+%29%5E2+%2B+30%2A%28+15%2F2+%29+%2B+17+ ALIGN=MIDDLE  ALT=\"+f%28+15%2F2+%29+=+-2%2A%28+15%2F2+%29%5E2+%2B+30%2A%28+15%2F2+%29+%2B+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28+15%2F2+%29+=+-225%2F2+%2B+225+%2B+17+ ALIGN=MIDDLE  ALT=\"+f%28+15%2F2+%29+=+-225%2F2+%2B+225+%2B+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28+15%2F2+%29+=+225%2F2+%2B+17+ ALIGN=MIDDLE  ALT=\"+f%28+15%2F2+%29+=+225%2F2+%2B+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28+15%2F2+%29+=+112.5+%2B+17+ ALIGN=MIDDLE  ALT=\"+f%28+15%2F2+%29+=+112.5+%2B+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28+15%2F2+%29+=+129.5+ ALIGN=MIDDLE  ALT=\"+f%28+15%2F2+%29+=+129.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "The maximum population was 129,500<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "1993 + 15/2 = 1993 + 7.5<BR>\n" );
document.write( "1993 + 7.5 = 2000<BR>\n" );
document.write( "The maximum was reached in 2000<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-2%2C+20%2C+-15%2C+150%2C+-2x%5E2+%2B+30x+%2B+17+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-2%2C+20%2C+-15%2C+150%2C+-2x%5E2+%2B+30x+%2B+17+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );