二次函数y=f(x)=ax~2+bx+c(a≠0)的图像(抛物线)关于直线x=-b/2a对称.如果有f(p)=f(q),且p≠q,则f(p+q)=c.简证如下:法1 f(p)=f(q),因为对称轴方程为x=-b/2a=(p+q)2,所以,p+q=-b/a.所以f(p+q)=f(-b/a)=a(- The image (parabola) of the quadratic function y = f (x) = ax ~ 2 + bx + c (a ≠ 0) is symmetric with respect to the straight line x = -b / 2a. Since p ≠ q, then f (p + q) = c. The proofs are as follows: Law 1 f (p) = f (q) because the symmetry axis equation is x = -b / 2a = (p + q) , p + q = -b / a. Therefore, f (p + q) = f (-b / a) = a