Let $P_2$ be the vector space of all polynomial functions of degree at most two from $\mathbb{R}$ to $\mathbb{R}$ and let $f_0,f_1,f_1: \mathbb{R} \rightarrow \mathbb{R}$ be the functions given by $$f_0(x)=1, \ f_1(x)=x, \ f_2(x)=x^2$$
a) Show that $B =(f_0,f_1,f_2)$ is an ordered basis of $P_2$.
b) Show that the function $T: P_2 ↦ P_2$ given by
$$T(f)(x)=f(x+1), \ \ x \in \mathbb{R}$$
is a linear transformation.
c) Find the matrix $A^{B,B}_T$.