document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388076>Question 388076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let function(x)be definedas f(x) =xx+bx+c, where bandc are real numbers<BR>\n" );
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document.write( "determine all pairs(b,c)such that /f(x)/ is less than equal to 8for all x in the interval. /1,9/ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275144 by </B><A HREF=/tutors/aboutme.mpl?userid=Jk22><B>Jk22(389)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Jk22><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=Jk22><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = xx+bx+c is a parabola open upside<BR>\n" );
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document.write( "values at the border : y1=b+c+1, y2=81+9b+c<BR>\n" );
document.write( "minimum at -b/2 value : ym=-b^2/4+c<BR>\n" );
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document.write( "|f(x)| is <=8 if all three value are <BR>\n" );
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document.write( "hence the conditions are : |b+c+1|<=8 |81+9b+c|<=8<BR>\n" );
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document.write( "if 1<-b/2<9 which is the same as : -2>b>-18, there should |-b^2/4+c|<8\r<BR>\n" );
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document.write( "hence the solution if : \r<BR>\n" );
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document.write( "{ (b,c) | |b+c+1|<=8 and |81+9b+c|<=8 and (|b^2/4-c|<=8 if b in [-18,-2]) }<BR>\n" );
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