How to do this on my Prime ?

[AlexFekken]

1 - The quickest way might be to determine the Lagrange polynomial:

lagrange([1 -2 3], [2 1 4])

(then simplify the result).

2 - If you really want to solve the linear equations then you can do that as follows:

linsolve([a+b+c=2 4*a-2*b+c=1 9*a+3*b+c=4], [a b c])

3 - Or if you want to imitate the approach in your second screenshot:

f(x):=a*x^2+b*x+c
solve({f(1)=2,f(-2)=1,f(3)=4},[a b c])