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Axis of Symmetry of a Parabola

Picture of the axis of symmetry

Picture of Axis of symmetry of a parabola

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

In Graph 2, what is the equation of the axis of symmetry?

Axis of Symmetry

It is the line $$ x = 2 $$

Problem 2

In Graph 3, what is the equation of the axis of symmetry?

Picture of Axis of Symmetry

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 .

Picture of Axis of Symmetry for 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} }} $
Picture of Axis of Symmetry for vertex form

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

What is the following parabola's axis of symmetry of $$ y = (x + 3)^2 + 4$$

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

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

Axis of Symmetry
Problem 4

What is the axis of symmetry of the parabola $$ y = (x - 3)^2 + 4 $$

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

Axis of Symmetry
Problem 5

What is the axis of symmetry of $$ y = (x - 1)^2 + 1 $$

Axis

Practice

finding axis of symmetry from Standard Form

Problem 6

What is the following parabola's axis of symmetry of $$ y =x^2 - 2x - 3 $$

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 $$ x = 1 $$

Axis of Symmetry
Problem 7

What is the following parabola's axis of symmetry of $$y =x^2 - 4x + 5 $$

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

Axis of Symmetry

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