Find Quadratic Line of Symmetry

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Find Quadratic Line of Symmetry

Quadratic line of symmetry
(Kelvinsong/Wikimedia Commons/CC0)

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.

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Find the Line of Symmetry Graphically

graph paper
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Find the line of symmetry of y = x2 + 2x with 3 steps.

  1. 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)
  2. What is the x-value of the vertex? -1
  3. 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.

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Use an Equation to Find the Line of Symmetry

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

x = -b/2a

Remember, a quadratic function has the following form:

y = ax2 + bx + c

Follow 4 steps to use an equation to calculate the line of symmetry for y = x2 + 2x

  1. Identify a and b for y = 1x2 + 2x. a = 1; b = 2
  2. Plug into the equation x = -b/2a. x = -2/(2*1)
  3. Simplify. x = -2/2
  4. The line of symmetry is x = -1.