Axis of Symmetry of a Parabola
The graph of aquadratic functionis 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 thevertex 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 ofusing 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.