Answer
It is a parabola.
See Graph I for the graphing of the equation.
Work Step by Step
For $x = -y^2 + 6y$, it can be rewritten as
$x = -y^2 +6y -9 +9$
$x = -(y^2 -6y +9) +9$
$x = -(y - 3)^2 + 9$
It is in the form of a parabola.
Sine the coefficient of $y^2$ is negative, the parabola opens to the left.
When x = 0, y = 0 or y = 6, the $y-intercepts$ are at 0 and 6.
The vertex is at (9, 3).
See Graph I for the graphing of the equation.