Satisfy f(x-2)=f(-x-2),

a(x-2)^2+b(x-2)+c=a(x+2)^2-b(x+2)+c

b=4a

The intercept of the image on the y axis is 1.

c= 1

The length of the line segment cut by the X axis is twice that of the root number 2.

X 1-x2=2 times the root number 2.

√[(b^2-4ac)/a^2]

=2√2

From the above, it can be concluded that:

a= 1/2

b=2

c= 1

y=( 1/2)x^2+2x+ 1

Only once, you can elaborate!