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 -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
For a quadratic function in standard form, , the axis of symmetry is a vertical line .
Example 1:
Find the axis of symmetry of the parabola shown.
The -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
The vertex of the parabola is .
So, the axis of symmetry is the line .
Example 2:
Find the axis of symmetry of the graph of using the formula.
For a quadratic function in standard form, , the axis of symmetry is a vertical line .
Here, and .
Substitute.
Simplify.
Therefore, the axis of symmetry is .