Symmetry in Algebraic Equations

The video tutorial explains how to determine if the graphs of equations are symmetrical about the x-axis, y-axis, or the origin. It covers three tests for symmetry: replacing y with -y for x-axis symmetry, replacing x with -x for y-axis symmetry, and replacing both x and y with their negatives for origin symmetry. The tutorial includes visual and algebraic verification methods, using examples like Y = X^3 - 2X and X^2 + 4Y^2 = 4 to illustrate the concepts.

What is the test for X-axis symmetry in a graph?

• Rotate the graph 180 degrees.

• Replace both X and Y with their negatives.

• Replace Y with -Y and check for equivalence.

• Replace X with -X and check for equivalence.

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CCSS.HSF.BF.B.3

How can you visually verify Y-axis symmetry in a graph?

• Rotate the graph 90 degrees.

• Fold the graph across the Y-axis.

• Check if the graph is a straight line.

• Fold the graph across the X-axis.

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CCSS.HSF.BF.B.3

What is the result of replacing X with -X in the equation Y = -X^4 + 4X^2 + 5?

• Y = -X^4 - 4X^2 + 5

• Y = -X^4 + 4X^2 + 5

• Y = X^4 - 4X^2 + 5

• Y = X^4 + 4X^2 + 5

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CCSS.HSF.BF.B.3

Which type of symmetry does the graph of Y = X^3 - 2X exhibit?

• No symmetry

• X-axis symmetry

• Y-axis symmetry

• Symmetry about the origin

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CCSS.HSF.BF.B.3

What happens when you replace X with -X in the equation Y = X^3 - 2X?

• The equation becomes Y = -X^3 + 2X.

• The equation remains unchanged.

• The equation becomes Y = X^3 + 2X.

• The equation becomes Y = -X^3 - 2X.

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CCSS.HSG.CO.A.4

What type of symmetry does the ellipse X^2 + 4Y^2 = 4 have?

• X-axis symmetry only

• Y-axis symmetry only

• Symmetry about the origin only

• All of the above

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CCSS.HSF.IF.A.1

How do you test for Y-axis symmetry in the equation X^2 + 4Y^2 = 4?

• Rotate the graph 90 degrees.

• Replace both X and Y with their negatives.

• Replace X with -X and check for equivalence.

• Replace Y with -Y and check for equivalence.

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CCSS.HSF.BF.B.3

What is the result of replacing Y with -Y in the equation Y^2 - 2Y^4 = 6X?

• Y^2 + 2Y^4 = 6X

• Y^2 - 2Y^4 = -6X

• Y^2 - 2Y^4 = 6X

• -Y^2 - 2Y^4 = 6X

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CCSS.HSF.IF.A.1

Does the equation Y^2 - 2Y^4 = 6X have Y-axis symmetry?

• Yes, it does.

• No, it does not.

• Only if Y is negative.

• Only if X is positive.

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CCSS.HSF.IF.A.1

What is the algebraic verification for X-axis symmetry in Y^2 - 2Y^4 = 6X?

• Rotate the graph 180 degrees.

• Replace X with -X and check for equivalence.

• Replace Y with -Y and check for equivalence.

• Replace both X and Y with their negatives.