Difficult# Tangent to a Quadratic

APCALC-EBKKEI

A line tangent to the graph of $f(x)={ ax }^{ 2 }+bx +12$ has its point of tangency at $x=1$.

If the tangent line has a slope of $-4$ and also contains the point $(0,\,11)$, which of the following equations could represent $f(x)$?