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Axis of Symmetry of a Parabola

 Axis of Symmetry 


Picture of Axis of symmetry of a parabola 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.

In the picture of on the left, the axis of symmetry is the line x =1.

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 the picture on the left, identify the axis of symmetry.
Answer



Problem 2) What is the axis of symmetry of the parabola on the left?
Answer

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

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

    Answer


    2) What is the axis of symmetry of the parabola
    y = (x – 3)² + 4
    Axis of Symmetry


    3) What is the axis of symmetry of
    y = (x–1)² + 1

    Axis of Symmetry
    Practice finding axis of symmetry from Vertex Form Equation

    1) What is the following parabola's axis of symmetry of
    y =x² −2x −3
    Answer
    1) What is the following parabola's axis of symmetry of
    y =x² −4x + 5 44
    Answer