Every parabola has an **axis of symmetry** which is the line that runs down its 'center'. This line divides the graph into two perfect halves.

*Explore how the graph and equation relate to the axis of symmetry*, by using our interactive program below.

### Identify Axis of Symmetry From Graph

It is the line $$ x = 2 $$

It is the line $$ x = -1 $$

### Axis of Symmetry Formula

There are two different formulas that you can use to find the axis of symmetry. One formula works when the parabola's equation is in vertex form and the other works when the parabola's equation is in standard form.

If your equation is in vertex form, then the axis of is:

x= h in the general vertex form equation y = (x-h)^{2} + k

If your equation is in standard form, then the formula for the axis of symmetry is:

$$ x = \frac {-b}{ 2a} $$ from the general standard form equation $$ y = ax^2 +bx + c $$

**Practice** finding axis

of symmetry from Vertex Form Equation

Since this equation is in vertex form,use the formula x = h

The line $$ x = -3 $$ is this parabola's axis of symmetry.

Since this equation is in vertex form,use the formula x = h

The axis of symmetry is the line $$ x = 3$$

**Practice**

finding axis of symmetry from Vertex Form Equation

Since this equation is in standard form, use the formula for standard form equation $$ x = \frac{ -b}{ 2a} $$

**Answer: **the axis of symmetry is the line $$ x = 1 $$

Since this equation is in standard form, use the formula for standard form equation x = -b/2a

**Answer: **the axis of symmetry is the line x = 2