SOLUTION: Let function(x)be definedas f(x) =xx+bx+c, where bandc are real numbers determine all pairs(b,c)such that /f(x)/ is less than equal to 8for all x in the interval. /1,9/

Algebra ->  Rational-functions -> SOLUTION: Let function(x)be definedas f(x) =xx+bx+c, where bandc are real numbers determine all pairs(b,c)such that /f(x)/ is less than equal to 8for all x in the interval. /1,9/      Log On


   

Question 388076: Let function(x)be definedas f(x) =xx+bx+c, where bandc are real numbers

determine all pairs(b,c)such that /f(x)/ is less than equal to 8for all x in the interval. /1,9/
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = xx+bx+c is a parabola open upside

values at the border : y1=b+c+1, y2=81+9b+c
minimum at -b/2 value : ym=-b^2/4+c

|f(x)| is <=8 if all three value are

hence the conditions are : |b+c+1|<=8 |81+9b+c|<=8

if 1<-b/2<9 which is the same as : -2>b>-18, there should |-b^2/4+c|<8
hence the solution if :
{ (b,c) | |b+c+1|<=8 and |81+9b+c|<=8 and (|b^2/4-c|<=8 if b in [-18,-2]) }