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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.

Math diagram

For a quadratic function in standard form, y = a x 2 + b x + c , the axis of symmetry is a vertical line x = b 2 a .

Example 1:

Find the axis of symmetry of the parabola shown.

Math diagram

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 2:

Find the axis of symmetry of the graph of y = x 2 6 x + 5 using the formula.

For a quadratic function in standard form, y = a x 2 + b x + c , the axis of symmetry is a vertical line x = b 2 a .

Here, a = 1 , b = 6 and c = 5 .

Substitute.

x = 6 2 ( 1 )

Simplify.

x = 6 2 = 3

Therefore, the axis of symmetry is x = 3 .

Math diagram

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