Axis of Symmetry (Parabola)
Definition

The axis of symmetry of a parabola is a line about which the parabola is symmetrical.



Vertex of a parabola

When the parabola is vertical, the line of symmetry is vertical.


Vertex of a vertical parabola

When a quadratic function is graphed in the coordinate plane, the resulting parabola and corresponding axis of symmetry are vertical.


Algebra

STANDARD FORM

The graph of the parabola represented by the quadratic function   y = a( x - p )2 + q   has an axis of symmetry represented by the equation of the vertical line   x = p.

Standard Form: Axis of Symmetry

GENERAL FORM

General Form: Axis of Symmetry

Click here to see how this formula is derived.

General Form: Axis of Symmetry

FACTORED FORM

Factored Form: Axis of Symmetry
Factored Form: Axis of Symmetry