Let the function be:

f(x) = ax^2 + bx + c

f(0) = c = 2

f(1) = a+b + 2 = 3........(1)

f(-1) = a - b + 2 = 3.

==> a= b+1 .........(2)

Now let us substitute (2) in (1)

==> a + b + 2 = 3

==> (b+1) + b + 2 = 3

==> 2b+3 = 3

==>2 b = 0

==> b =0

==> a = b+1 = 0 +1 = 1

==> a = 1 b = 0 c= 2

==> f(x) = 1*x^2 + 0*x + c

==> **f(x) = x^2 + 2**

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