Newton's and Lagrange form's of interpolating polynomial Can someone hint me on this one?

Question: Find the Lagrange and Newton forms of interpolating polynomial for these data points $(-1,0),(0,1), (2,3)$. Write both polynomials in the form $a x^2+bx+c$ to verify that they are identical as functions.

My incomplete solution:
I will skip all my working as to how I get my Lagrange and Newton forms of interpolating polynomial because that ain't THE problem here.
Lagrange form: $P(x)= -\frac1 2 (x+1)(x-2) + \frac 1 2 x(x+1)$
Newton form $N(x) = (x+1)$
The question is how will I put both of these in the form $a x^2+bx+c$ and show that they are identical as functions??
ANY HINTS??

Just expand the first one out. The main point is that in the Lagrange form, the first term gives a $-x^2/2$ and the second gives a $x^2/2$, and the two cancel, giving a linear function. Newton just gives a linear function in the first place.
Alternately, you can factor the $x+1$ from both terms and simplify. The result is the same.
