Given the function f (x) = x2 + ax + 3, when x ∈ [- 2,2], f (x) ≥ A is constant and the range of a is obtained Can we use the method of variable separation?

Given the function f (x) = x2 + ax + 3, when x ∈ [- 2,2], f (x) ≥ A is constant and the range of a is obtained Can we use the method of variable separation?

tolerable.
x^2+ax+3>=a
a(1-x)