Answer
$${\text{ parabola}}$$
Work Step by Step
$$\eqalign{
& x - 1 = - 3{\left( {y - 4} \right)^2} \cr
& {\text{Divide both sides by }} - 3 \cr
& - \frac{1}{3}\left( {x - 1} \right) = {\left( {y - 4} \right)^2} \cr
& or \cr
& {\left( {y - 4} \right)^2} = - \frac{1}{3}\left( {x - 1} \right) \cr
& {\text{The equation is written in the form }}{\left( {y - k} \right)^2} = 4p\left( {x - h} \right) \cr
& {\text{Therefore,}} \cr
& {\text{The graph of the equation }}x - 1 = - 3{\left( {y - 4} \right)^2}{\text{ is a parabola}} \cr} $$
