Determine the type of symmetry (symmetry with respect to the x axis, y axis, or origin) exhibited by the graph of the equation: x ² + 5 y = -6. A) symmetry with respect to the x axis B) symmetry with respect to the y axis C) symmetry with respect to the origin

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Quizplus · Accepted Answer

If we replace x with -x, the equation becomes (-x)^2 + 5y = -6, which simplifies to x^2 + 5y = -6. Since this is not the same as the original equation, there is no symmetry with respect to the origin. However, if we replace y with -y, the equation becomes x^2 + 5(-y) = -6, which simplifies to x^2 - 5y = -6. This is the same as the original equation, so there is symmetry with respect to the y axis. There is no symmetry with respect to the x axis.

Determine the Type of Symmetry (Symmetry with Respect to the X