Question

设二次函数f(x)满足f(x+2)=f(2-x),且f(x)=0的两实根平方和为10,图像过点（0,3),求f(x)的解

Answer 1

x=2是对称轴

f(x)=a(x-2)^2+b=ax^2-4ax+4a+b

f(0)=3 4a+b=3

10=x1^2+x2^2=(x1+x2)^2-2x1x2=16-2(4a+b)/a

a=1 b=-1

f(x)=(x-2)^2-1