Determine the second grade function if f(-1)=1, f(0)=1, f(1)=3.

f(x) = ax^2+bx+c be the 2nd degree
function.

Then

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

f(0) = ao^2+b*0^2+c = 1.
Or c = 1.............(2)

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

From (2) c = 1. So we rewrite (1) and
as:

a-b+1 =1 Or a-b =
0...........(4)

a+b+1 = 3. Or a+b =
2.......'(5)

Add (4) and (5) : 2a = 2. So a =1. So from (1)
a-b =0, 1-b = 0. or b=1.

Therefore a=b=c=1
.

So f(x) = ax^2+bx+c is the required second degree
function.