How to Graph a Horizontal Parabola
Work with the equation to find the axis of symmetry, focal distance, and directrix.
To find the axis of symmetry start with the vertex. The vertex of this parabola is (3, 1). The axis of symmetry is at y = v, so for this example, it is at y = 1.
For the equation given, a = 1/8, and so the focal distance is 2. Add this value to h to find the focus: (3 + 2, 1) or (5, 1).
To find the directrix, subtract the focal distance from Step 2 from h to find the equation of the directrix. Because this is a horizontal parabola and the axis of symmetry is horizontal, the directrix will be vertical. The equation of the directrix is x = 3 – 2 or x = 1.