Question

设f(x)是定义在R上的偶函数,当0≦x≦2时,y=x,当x＞2时,y=f(x)的图像是顶点为P(3,4),过点A(2,

Answer 1

x>2时,f(x)=a(x-3)^2+4

x=2时,y=2,a(2-3)^2+4=2,

a=-2,

f(x)=-2(x-3)^2+4 x>2

x2,

f(-x)=-2(-x-3)^2+4 ,

即f(x)=-2(x+3)^2+4 x