Let $T: P_3 \rightarrow P_3$ be the linear transformation satisfying $$T(1)=2 x^2 + 1, \ \ \ T(x)=2 x + 9, \ \ \ T(x^2)=-4 x^2 + x - 2.$$ Find the image of an arbitrary quadratic polynomial $ax^2 + bx + c$.

$T(ax^2 + bx + c)=$ .