If the quadratic function f (x), when x = 1 / 2, the maximum value of F (x) is 25, the equation f (x) = 0 and the sum of two cubes is 19, then f (x)

Let f (x) = a (x-1 / 2) ^ 2 + 25 = ax ^ 2-ax + A / 4 + 25 = 0x1 + x2 = 1x1x2 = A / 4 + 25x1 ^ 3 + x2 ^ 3 = (x1 + x2) (x1 ^ 2-x1x2 + x2 ^ 2) = (x1 + x2) ((x1 + x2) ^ 2-3x1x2) = 1-3x1x2 = 1-3a / 4-75 = 19, then a = - 124f (x) = - 124 (x-1 / 2) ^ 2 + 25 = - 1

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