## Find Quadratic Line of Symmetry

A parabola is the graph of a quadratic function. Each parabola has a **line of symmetry**. Also known as the **axis of symmetry**, this line divides the parabola into mirror images. The line of symmetry is always a vertical line of the form *x* = *n*, where *n* is a real number.

This tutorial focuses on how to identify the line of symmetry. Learn how to use either a graph or an equation to find this line.

## Find the Line of Symmetry Graphically

Find the line of symmetry of *y* = *x*^{2} + 2*x* with 3 steps.

- Find the vertex, which is the lowest or highest point of a parabola.
*Hint*: The line of symmetry touches the parabola at the vertex.**(-1,-1)** - What is the
*x*-value of the vertex?**-1** - The line of symmetry is
*x*= -1

*Hint*: The line of symmetry (for any quadratic function) is always ** x = n** because it is always a vertical line.

## Use an Equation to Find the Line of Symmetry

The axis of symmetry is also defined by the following equation:

x= -b/2a

Remember, a quadratic function has the following form:

y=ax^{2}+bx+c

Follow 4 steps to use an equation to calculate the line of symmetry for *y* = *x*^{2} + 2*x*

- Identify
*a*and*b*for*y*=**1***x*^{2}+**2***x*.**a = 1; b = 2** - Plug into the equation
*x*= -*b*/2*a.***x = -2/(2*1)** - Simplify.
**x = -2/2** - The line of symmetry is
.*x*= -1