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AP® Calculus AB-BC

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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 $f(x)$?

A

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

B

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

C

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

D

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