﻿ Axis of Symmetry of a Parabola. How to find axis from equation or from a graph. To find the axis of symmetry ...

# Axis of Symmetry of a Parabola

Picture of the axis of symmetry

Every parabola has an axis of symmetry which is the line that divides the graph into two perfect halves.

On this page, we will practice drawing the axis on a graph, learning the formula, stating the equation of the axis of symmetry when we know the parabola's equation

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

### Identify Axis of Symmetry From Graph

##### Problem 1

It is the line $$x = 2$$

##### Problem 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 the standard form $$y = ax^2 + bx + c$$ , then the formula for the axis of symmetry is: $\red{ \boxed{ x = \frac {-b}{ 2a} }}$

If your equation is in vertex form $$y = (x-h)^2 + k$$ , then the formula for axis is $\red { \boxed{ x = h}}$

### Interactive Demonstration of Axis of Symmetry

Explore the relationship between the axis of symmetry and graph of a parabola by changing the values of a, b and c of the parabola plotter below

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### Practice finding axis of symmetry from Vertex Form Equation

##### Problem 3

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

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

##### Problem 4

Since this equation is in vertex form, use the formula $$x = h$$
The axis of symmetry is the line $$x = 3$$

### Practicefinding axis of symmetry from Standard Form

##### Problem 6

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 $$x = 1$$

##### Problem 7

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