It is known that the quadratic function f (x) satisfies f (4-x) = f (x), the length of the line cut on the x-axis is 6, and the function image passes (3,8). The analytic expression of F (x) is obtained Modify "and function image (3, - 8),"

It is known that the quadratic function f (x) satisfies f (4-x) = f (x), the length of the line cut on the x-axis is 6, and the function image passes (3,8). The analytic expression of F (x) is obtained Modify "and function image (3, - 8),"

The quadratic function f (x) satisfies f (4-x) = f (x), which indicates that its axis of symmetry is x = 2
If the length of the line segment cut on the x-axis is 6, then the coordinates of the two intersections with the x-axis are (2 + 6 / 2,0) and (2-6 / 2,0), namely (5,0) and (- 1,0)
So let f (x) = a (X-5) (x + 1)
If the function image is over (3, - 8), the coordinates are substituted into: - 8 = a (3-5) (3 + 1)
A = 1
The equation is f (x) = (X-5) (x + 1) = x ^ 2-4x-5