Answer
$${\text{parabola}}$$
Work Step by Step
$$\eqalign{
& {x^2} - 6x + y = 0 \cr
& {\text{Subtract }}y{\text{ from both sides of the equation}} \cr
& {x^2} - 6x = - y \cr
& {\text{Multiply both sides by }} - 1 \cr
& - \left( {{x^2} - 6x} \right) = y \cr
& {\text{Complete the square and factor}} \cr
& - \left( {{x^2} - 6x + 9} \right) = y - 9 \cr
& - {\left( {x - 3} \right)^2} = y - 9 \cr
& {\left( {x - 3} \right)^2} = - \left( {y - 9} \right) \cr
& {\text{The equation is written in the form }}{\left( {x - h} \right)^2} = 4p\left( {y - k} \right) \cr
& {\text{Therefore,}} \cr
& {\text{The graph of the equation }}{x^2} - 6x + y = 0{\text{ a parabola}} \cr} $$
