Answer
$${\text{ parabola}}$$
Work Step by Step
$$\eqalign{
& 11 - 3x = 2{y^2} - 8y \cr
& {\text{Divide both sides of the equation by 2}} \cr
& \frac{1}{2}\left( { - 3x + 11} \right) = {y^2} - 4y \cr
& {\text{Complete the square and factor}} \cr
& \frac{1}{2}\left( { - 3x + 11} \right) + 4 = {y^2} - 4y + 4 \cr
& - \frac{3}{2}x + \frac{{11}}{2} + 4 = {\left( {y - 2} \right)^2} \cr
& - \frac{3}{2}x + \frac{{19}}{2} = {\left( {y - 2} \right)^2} \cr
& {\left( {y - 2} \right)^2} = - \frac{3}{2}\left( {x - \frac{{19}}{3}} \right) \cr
& {\text{The equation is written in the form }}{\left( {y - k} \right)^2} = 4p\left( {x - h} \right) \cr
& {\text{Therefore,}} \cr
& {\text{The graph of the equation }}11 - 3x = 2{y^2} - 8y{\text{ is a parabola}} \cr} $$
