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It is known that the quadratic function FX = AX2 + BX (a, B are constants, and a is not equal to 0) satisfies the following conditions: F (- x + 5) = f (x-3), and the equation f (x) = x has real roots (1) Find the analytic expression of F (x); (2) whether there are real numbers m, n (m < n), so that the definition field and value field of F (x) are [M, n] and [3M, 3N]? Request the value of M, n
From F (- x + 5) = f (x-3), we can see that the axis of symmetry is x = 1, so B / (- 2A) = 1 b = - 2A; because ax ^ 2 + BX = x, that is, ax ^ 2 + (B-1) x = 0 has multiple roots, obviously X1 = x2 = 0, so B = 1, a = - 1 / 2, so f (x) = - 1 / 2x ^ 2 + X2F
RELATED INFORMATIONS
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