Given that the maximum value of quadratic function y = f (x) is equal to 4, and f (3) = (- 1) = 0 (1), find the analytic expression of F (x); (2) write the monotone interval of F (x)

Given that the maximum value of quadratic function y = f (x) is equal to 4, and f (3) = (- 1) = 0 (1), find the analytic expression of F (x); (2) write the monotone interval of F (x)

The maximum value of F (x) is 4, and f (3) = (- 1) = 0. The axis of symmetry is x = 2 extreme point (2,4) and passes through (- 1,0) and (3,0), so the equation is ax ^ 2 + BX + C = y. three points (2,4) (- 1,0) (3,0) are substituted: B = 4 / 9, a = - 8 / 9, C = 12 / 9, so the equation is - 8 / 9 * x ^ 2 + 4 / 9 * x + 12 / 9 = y monotonic interval: from negative infinity to 2 is monotonic increasing, and from 2 to positive infinity is monotonic decreasing