Symmetry of a Parabola

One aspect of a parabola that will help you with graphing and writing the equation is symmetry. We talked about the axis of symmetry. The axis of symmetry of a parabola that has a vertex at the origin is either the y-axis, if the parabola opens upward or downward, or the x-axis, if the parabola opens right or left.

If the parabola has a vertex at (h, k), the axis of symmetry is defined at x = h for parabolas that open upward or downward, or y = k for parabolas that open right or left.

Remember that the axis of symmetry splits the parabola into two equal pieces.

Parabolas can also be described as having horizontal or vertical symmetry. If the line of symmetry is a horizontal line, y = 2, for example, the parabola has horizontal symmetry.  If the line of symmetry is a vertical line, x = 5, for example, the parabola has vertical symmetry.

The parabola graphed below has the line x = 1 as its line of symmetry.  Notice that to the left and to the right of this line, the parabola is a mirror image of itself.  This parabola has vertical symmetry.