Hi!! Help with some algebra!​

If f(0)=0, f(1)=2, f(2)=5 and f(x)=ax^2+bx+c, what is the value of f(3)

If f(0) = 0, then c  = 0

So we have these two equations  for f(1)  and f(2)

a(1)^2  + b(1)  = 2   →   a + b   = 2       (1)

a(2)^2  + b(2)  = 5   →  4a + 2b = 5      (2)

Multiply (1) by - 2   →  -2a - 2b = -4        add this to (2)

2a  = 1     →   a = 1/2

And subbing this into (1) to find b

1/2 + b  = 2      →   b = 3/2

So our function is

f(x)  =  (1/2)x^2  + (3/2)x

So   f(3)  =   (1/2) (3)^2  + (3/2) (3)  =   9/2  + 9/2  =  18/2  = 9