Determine the quadratic function if f(1)=3 , f(0)=2 , f(-1)=3.

Let the quadratic equation be  f(x) =
ax^2+bx+c.

The values of f(x) for 3 values are given.
Substituting this  in the equation, we get:

f(1) = 3 :
 a*1^2+b*1+c = a+b+c =3...(1)

f(0) = 2:  a*0^2+b*0+c =  c
=2....(2)

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

(1)+(3) : 2a+2c =6.  a+c = 3. but c = 2 from
(2). So a = 3-2 =1.

So a=1, c =2. Therefore a+b+c  = 1+b+2
=3 from (1). So b = 3-3 = 0.

Therefore a = 1, b =0 and c
=2.

So f(x) = ax+bx+c  = x+0x+2 =
x+2.

f(x) =
x+2.

f