Answer
It is a parabola.
See Graph I for the graphing of the equation.
Work Step by Step
For $x = y^2 + 4y -1$, it can be rewritten as
$x = y^2 + 4y +4 -1 -4$
$x = (y+2)^2 -5$
It is in the form of a parabola.
Since the coefficient of $y^2$ is positive, the parabola opens to the right.
When $y = 0, x = -1$, the $x-intercept$ is at -1.
The vertex is at (-5, -2).
See Graph I for the graphing of the equation.