It is known that the function y = f (x) is a quadratic function, and f (- 3 / 2 + x) = f (- 3 / 2-x), f (- 3 / 2) = 49, and the difference between the two real roots of the equation f (x) = 0 is equal to 7 Finding the analytic expression of quadratic function

It is known that the function y = f (x) is a quadratic function, and f (- 3 / 2 + x) = f (- 3 / 2-x), f (- 3 / 2) = 49, and the difference between the two real roots of the equation f (x) = 0 is equal to 7 Finding the analytic expression of quadratic function

From F (- 3 / 2 + x) = f (- 3 / 2-x), - B / 2A = - 3 / 2 F (- 3 / 2) = 49 has (4ac-b ^ 2) / 4A = 49 Let f (x) = ax ^ 2 + BX + C, Let f (x) = 0b ^ 2-4ac > 0. According to WIDA's theorem, there is X1 + x2 = - B / A Three formula x1x2 = C / a The results show that a, B, C, a, B, C, a, B, C, B, C, C, C, C, C, C, C, C, C, C, C, C, C, C, C, C, C, C, C, C, C, C, C, C, C