Answer:
Symmetry is more of a geometrical than an algebraic concept but, as mentioned in the previous two pages, the subject of symmetry does come up in a couple of algebraic contexts. When you're graphing quadratics, you may be asked for the parabola's axis of symmetry. This is usually just the vertical line x = h, where "h" is the x-coordinate of the vertex, (h, k). That is, a parabola's axis of symmetry is usually just the vertical line through its vertex. The other customary context for symmetry is judging from a graph whether a function is even or odd. If f(−x) = −f(x), then the graph of f(x) is symmetrical with respect to . A function symmetrical with respect to the y-axis is called an even function. A function that is symmetrical with respect to the origin is called an odd function.
Note: By definition, no function can be symmetric about the x-axis (or any other horizontal line), since anything that is mirrored around a horizontal line will violate the Vertical Line Test.
Symmetry
On the other hand, a function can be symmetric about a vertical line or about a point. In particular, a function that is symmetric about the y-axis is also an "even" function, and a function that is symmetric about the origin is also an "odd" function. Because of this correspondence between the symmetry of the graph and the evenness or oddness of the function, "symmetry" in algebra is usually going to apply to the y-axis and to the origin.
