Determine the second grade function if f11 f01 f13Solutionfx

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

Solution

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.