
Given our comments above, this equation yields a parabola. (Note that this equation only has one square term. This indicates that we have a parabola here, as opposed to an ellipse or hyperbola.)
The value of d in this case is fairly clear; namely,

The vertex of this parabola is at
and the axis of this parabola is
vertical (since the variable x is the squared variable.) Thus, the focus
of this parabola is situated at the point
and the directrix is
the horizontal line 2 units below the vertex. Thus, the equation of the
directrix is given by

See Figure P7 for a sketch of this parabola.

James A. Sellers