x = -1/2y squared - y - 4
Re-write the equation into the vertex-directrix-form:
The vertex has the coordinates
Therefore the directrix has the equation d:
With your need for x-axis and y-axis I assume that you mean the x and y intercepts of the parabola:
x-intercept: y = 0:
y-intercept: x = 0:
The LHS is negative, the RHS is a square - but a square can't be negative and therefore there doesn't exist any y-intercept.
Another attempt: The vertex is left of the y-axis and the parabola opens to left. Therefore the parabola and the y-axis can't have a common point. Thus: No y-intercept.