The function f (x) = ax ^ 2 + 2 (A-3) + 1 is a decreasing function in the interval (- 2, + ∞). Find the value range of real number a!

The function f (x) = ax ^ 2 + 2 (A-3) + 1 is a decreasing function in the interval (- 2, + ∞). Find the value range of real number a!

When a = 0, the original formula is f (x) = - 6x + 1, which is obviously a decreasing function; when a ≠ 0, the derivative of the original formula is f '(x) = 2aX + 2 (A-3), which is less than or equal to 0 on (- 2, + ∞); when a is greater than 0, f' (x) is an increasing function, which obviously does not satisfy the condition; when a is less than 0, f '(x) is a decreasing function, as long as the maximum value of F' (x) is less than, etc