Example 2

Let us now look at the equation of a parabola with horizontal axis. Consider the equation

Again, realize that this is a parabola (as opposed to an ellipse or a hyperbola) because it only has one squared term (as opposed to two). Because the y is squared instead of the x, we automatically know that this parabola has a horizontal axis. The only other question dealing with orientation is whether the parabola opens to the left or to the right.

We note here that

This indicates that the parabola will indeed open to the left. The vertex is again , as in the first example, and the focus will now occur at the point . Finally, the equation of the directrix is

See Figure P8 for the graph of this parabola.