Question 388076
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]) }