Functions and Their Graphs · Superchallenge problem

The graph of $y=f(x)$ is transformed in three steps, in this order: it is reflected across the $y$-axis; then shifted $4$ units to the right; then compressed horizontally by a factor of $\tfrac12$ (each point $(x,y)$ moves to $(\tfrac{x}{2},y)$). The final graph is $y=4x^2-4x+3$. Find $f(x)$, written in the form $ax^2+bx+c$.