Axis of Symmetry of a Parabola

The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.

For a quadratic function in standard form, y = ax2 + bx + c, the axis of symmetry is a vertical line

Example:

Find the axis of symmetry of the parabola shown.

The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.

The vertex of the parabola is (2, 1).

So, the axis of symmetry is the line x = 2.

Example:

Find the axis of symmetry of the graph of y = x2 – 6 x + 5 using the formula.

For a quadratic function in standard form, y = ax2 + bx + c, the axis of symmetry is a vertical line

Here, a = 1, b = –6, and c = 5.

Substitute.

Simplify.

Therefore, the axis of symmetry is x = 3.