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Quadratic function, f (x) = AX2 + BX + C, f F (x) = AX2 + BX + C, f (x) = f (2-x), f (0) = 3, f (1) = 2.1. Find the analytic formula of function. 2. F (x) belongs to the maximum value of [- 1,2] in X
F (0) = 3, C = 3, f (1) = 2, a + B = - 1
F (2) = f (0) = 4A + 2B + 3 = 3, so a = 1, B = - 2. The analytic expression of the forced function is f (x) = x ^ 2-2x + 3
2. F (x) = (x-1) ^ 2 + 1. Because the axis of symmetry is between [- 1,2], the minimum value is the value on the axis of symmetry, that is, the minimum value is 1; the maximum value is obtained at - 1 or at 2. According to the distance from the axis of symmetry, we can know that it is obtained at - 1, that is, the maximum value is 5
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