It is known that y = f (x) is a quadratic function and f (- 2 / 3-x) = f (- 2 / 3 + x), which holds for X ∈ R, F (- 2 / 3) = 49, the difference between the two real roots of the equation f (x) is only 7, (1) find the analytic expression of quadratic function, (2) find the maximum value of F (x) in the interval [T, t + 1], T is a random number, not a fixed value There are three cases where t + 1 is on the left, right and middle of the axis of symmetry

It is known that y = f (x) is a quadratic function and f (- 2 / 3-x) = f (- 2 / 3 + x), which holds for X ∈ R, F (- 2 / 3) = 49, the difference between the two real roots of the equation f (x) is only 7, (1) find the analytic expression of quadratic function, (2) find the maximum value of F (x) in the interval [T, t + 1], T is a random number, not a fixed value There are three cases where t + 1 is on the left, right and middle of the axis of symmetry

, f (- 2 / 3-x) = f (- 2 / 3 + x), so the symmetry axis is - 2 / 3, f (- 2 / 3) = 49, that is, the maximum value is 49 A = - 4, so the analytical formula is y = - 4 (x + 2 / 3) ^ 2 + 49
2. Because the opening is downward, it increases monotonically on the left side of the axis and decreases monotonically on the right side