Discriminant: b 2-4a (c+a) > =0
b^2+4ab>； =0
B & lt=-4a or b & gt=0.
Function symmetry axis x=-b/2a
When b & gt=0, the symmetry axis is -b/2a.
So the function is increasing function at (0, +∞).
When b & lt=-4a
Symmetry axis:-b/2a > =2
Note that f( 1)=a+b+c=0.
So x= 1 is a root of ax 2+bx+c = 0.
Because1* x2 = c/a.
So the other one is less than 0.
The symmetry axis cannot be greater than or equal to 2.
So b < =-4a doesn't matter.
So the function is increasing function at (0, +∞).
2。 g(x)=ax^2+2bx+c
According to the first question: b & gt=0.
|x 1-x2|= radical sign [(x 1+x2) 2-4x 1x2]
= radical sign [4b 2/a 2-4c/a]
= radical sign [4b 2/a 2+4b/a+4]
=2 root number [b 2/a 2+b/a+ 1]
Let b/a=t, t>0.
|x 1-x2|=2 radical [(t+ 1/2) 2+3/4]
So |x 1-x2| >=2 root number [(0+ 1/2) 2+3/4] = 2.