I think this might be : f(x) = ax^2 + bx + c
if f(1) = 5, f(2) = 8 and f(x) = ax^2+bx+2, what is the value of f(3)
f(1) = a + b + 2 = 5 ⇒ 2a + 2b + 4 = 10 (1)
f(2) = 4a + 2b + 2 = 8 (2) subtract (1) from (2) and we have that
2a - 2 = -2 add 2a to both sides
2a = 0
a = 0
And we can find b as
2(0) + 2b + 4 = 10
2b = 6
b = 3
So....the function is just
f(x) = 3b + 2
f(3) = 3(3) + 2 = 11