33 . In the \( x y \)-plane, the point \( (3,6) \) lies on the graph of the function \( f(x)=3 x^{2}-b x+12 \). What is the value of \( b \) ?

To find the value of \( b \), we can substitute the point \( (3, 6) \) into the function \( f(x) = 3x^2 - bx + 12 \). Substituting \( x = 3 \) and \( f(3) = 6 \): \[ 6 = 3(3^2) - b(3) + 12 \] Calculating \( 3(3^2) \): \[ 6 = 3(9) - 3b + 12 \] \[ 6 = 27 - 3b + 12 \] \[ 6 = 39 - 3b \] Now, subtract 39 from both sides: \[ 6 - 39 = -3b \] \[ -33 = -3b \] Dividing both sides by -3 gives: \[ b = 11 \] So, the value of \( b \) is \( \boxed{11} \).