SAT Mathematics Practice Test 2

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