Upgrade to access all content for this subject

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 $f(x)$?

$f(x)=x^2-6x+12$

$f(x)=-x^2+6x+12$

$f(x)={ -3x }^{ 2 }+2x+12$

$f(x)=3x^2 -2x + 12$