Lagrange interpolation polynomial

[allaputa]

Hello everyone
Here is my problem
lagrange interpolation polynomial across the points(x0,y0),(x1,y1) and (x2,y2) is given by y0L0(x) + y1L1(x) + y2L2(x)

where L0(x)=-x and L1(x)=x ^2 + x
Therefore L2(x) is given by
I tried it but i could'nt crack it

 

[radou]

The polynomial $$L(x)=\sum_{k=0}^n f(x_{k}) \prod_{i=0, i \neq k}^n \frac{x-x_{i}}{x_{k}-x_{i}}$$ is called the Lagrangian interpolation polynomial for a function f and the points $$x_{0}, x_{1}, ..., x_{n}$$, and it has the same values as the function f in these points. So, all you have to do is find your function and your points.