document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919253>Question 919253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I need help on my word problem homework. Would someone kindly help me please.Please show me the steps on how to solve the problem as well. Thank you.\r<BR>\n" );
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document.write( "Between 1989 and 1998, the population of small town, USA (in thousands) can be modeled by f(x)=0.8x^2-12.8x+54.2, where x=0 represents 1989. Based on this model, in what year did the population of small town reach its minimum?\r<BR>\n" );
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document.write( "My teacher said that the answer is: 1997\r<BR>\n" );
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document.write( "Would you please show me how he got the answer. Than you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557603 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=557603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In general, the min of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > is when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is assuming <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3E+0 ALIGN=MIDDLE  ALT=\"a+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C+0 ALIGN=MIDDLE  ALT=\"a+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we'll have a max and not a min.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0.8x%5E2-12.8x%2B54.2 ALIGN=MIDDLE  ALT=\"f%28x%29=0.8x%5E2-12.8x%2B54.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in that form where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+0.8 ALIGN=MIDDLE  ALT=\"a+=+0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-12.8 ALIGN=MIDDLE  ALT=\"b+=+-12.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We don't need c in this case.\r<BR>\n" );
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document.write( "Plug the values in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%28-12.8%29%2F%282%2A0.8%29 ALIGN=MIDDLE  ALT=\"x+=+-%28-12.8%29%2F%282%2A0.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8 ALIGN=MIDDLE  ALT=\"x+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Recall that x = 0 represents 1989. So x = 1 represents 1989+1 = 1990, etc etc\r<BR>\n" );
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document.write( "x = 8 means 1989 + 8 = 1997\r<BR>\n" );
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document.write( "So 8 years after the starting point of 1989, ie in the year 1997, the population is at the minimum.\r<BR>\n" );
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document.write( "If you want to know this min population value, plug it back into f(x) and evaluate.\r<BR>\n" );
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document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
document.write( "Feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a><BR>\n" );
document.write( "or you can visit my website here: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a>\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim  </SPAN>\n" );
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