Let the minimum value of function f (x) = x2-2x-1 in the interval [T, t + 1] be g (T), and find the range of G (T)

Let the minimum value of function f (x) = x2-2x-1 in the interval [T, t + 1] be g (T), and find the range of G (T)

∵ f (x) = x2-2x-1 = (x-1) 2-2, ∵ axis of symmetry x = 1, vertex coordinates (1, - 2), as shown in the figure; f (x) monotonically decreases on (- ∞, 1), monotonically increases on (1, + ∞). When 0 ≤ t ≤ 1, G (T) = - 2; when t ≥ 1, G (T) = f (T) = T2 -

The quadratic coefficient a of quadratic function f (x) is known, and the solution set of inequality f (x) > - x is (1,2). If the maximum value of F (x) is a positive number, then the value range of a is______

Let f (x) = AX2 + BX + C, (a < 0), the two roots of the equation f (x) = - X are 1, 2, that is, AX2 + (B + 1) x + C = 0, the two roots are 1, 2. The inequality of a is obtained by eliminating B and C. the solution of a is obtained by eliminating B and C