It is given that the function
f(x) passes through the point (3, 6). Thus, if x = 3, the value of f(x) is 6 (since the graph of
f in the xy-plane is the set of all points
(x,f(x)). Substituting 3 for x and 6 for
f(x) in
f(x)=3x2−bx+12 gives
6=3(3)2−b(3)+12. Performing the operations on the right-hand side of this equation gives
6=3(9)−3b+12=27−3b+12=39−3b
. Subtracting 39 from each side of
6=39−3b gives
−33=−3b, and then dividing each side of
−3b=−33 by
−3 gives the value of
b as
11.