Find the matrix $f$ with respect of the standard basis of $P_2$ and $\mathbb{R}^3$

Question

I have the following: $V = P_2(\mathbb{R})$, $W = \mathbb{R}^3$, and a mapping $f: V \to W$ defined by $$ f(a + bx + cx^2) = \begin{bmatrix} a \\ b \\ c \end{bmatrix}. $$ Now I need to find the matrix $f$ with respect to the bases for $P_2$ which is $\{1, x, x^2\}$ and for $\mathbb{R}^3$, which is $$ \left\{ \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}, \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}, \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \right\}. $$ Every example that I could found wasn't of this form so I am kinda confused how this will be solved one of my thoughts was that for every $f(1)$, $f(x)$ and $f(x^2)$ the answer would be $\mathbf{e}_1$, $\mathbf{e}_2$, and $\mathbf{e}_3$, respectively, but I am not sure if this is correct or how to prove it. Any advice would be appreciated.