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Published byAvery Porter Modified over 3 years ago

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Checking an equation for symmetry

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Types of symmetry Three types of symmetry 1.Symmetry with respect to the y-axis (vertical) 2.Symmetry with respect to the x-axis (horizontal) 3.Symmetry with respect to the origin

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Checking for symmetry with respect to the y-axis In the original equation, replace x with – x, and simplify. If the result is the original equation, there is symmetry about the y- axis. Example 1.y = x 2 – 2 y = (-x)2 – 2Substitute –x for x y = x 2 – 2Simplify There is symmetry about the y-axis.

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Checking for symmetry with respect to the y-axis Try this one. 1.y = 3 – 2x y = 3 - 2(-x) y = 3 + 2x There is not symmetry about the y-axis.

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Check for symmetry about the x- axis In the original equation, replace y with – y, solve for y. If the new equation is the same, there is symmetry about the x- axis. 1.y2 = x + 4 (-y)2 = x + 4 y2 = x + 4 There is symmetry about the x-axis.

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Check for symmetry about the x- axis Try this one. 1.y = x 3 – 2x (-y) = x 3 – 2x y = -x 3 + 2x There is not symmetry about the x-axis.

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Checking for symmetry about the origin In the original equation, substitute –x for x and –y for y, then simplify the equation. If the new equation is the same as the original, there is symmetry about the origin. 1.y = x 3 – 4x -y = (-x) 3 – 4(-x) -y = -x 3 + 4x y = x 3 – 4x There is symmetry about the origin.

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Checking for symmetry about the origin Try this one. 1.y 2 = x – 1 (-y) 2 = (-x) – 1 y 2 = -x – 1 There is no symmetry about the origin.

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