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=a x 2 +bx+c , the axis of symmetry is a vertical line x= b 2a .

Example 1:

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 2:

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

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

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 .