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  2. Symmetry in mathematics - Wikipedia

    en.wikipedia.org/wiki/Symmetry_in_mathematics

    Geometrically speaking, the graph face of an even function is symmetric with respect to the y-axis, meaning that its graph remains unchanged after reflection about the y-axis. Examples of even functions include |x|, x 2, x 4, cos(x), and cosh(x).

  3. Parabola - Wikipedia

    en.wikipedia.org/wiki/Parabola

    Suppose a system of Cartesian coordinates is used such that the vertex of the parabola is at the origin, and the axis of symmetry is the y axis. The parabola opens upward. It is shown elsewhere in this article that the equation of the parabola is 4fy = x 2, where f is the focal length. At the positive x end of the chord, x = ⁠ c / 2 ⁠ and y ...

  4. Symmetric graph - Wikipedia

    en.wikipedia.org/wiki/Symmetric_graph

    A t-transitive graph is a graph such that the automorphism group acts transitively on t-arcs, but not on (t + 1)-arcs. Since 1-arcs are simply edges, every symmetric graph of degree 3 or more must be t-transitive for some t, and the value of t can be used to further classify symmetric graphs.

  5. Cartesian coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cartesian_coordinate_system

    Each axis is usually named after the coordinate which is measured along it; so one says the x-axis, the y-axis, the t-axis, etc. Another common convention for coordinate naming is to use subscripts, as (x 1, x 2, ..., x n) for the n coordinates in an n-dimensional space, especially when n is greater than 3 or unspecified.

  6. Even and odd functions - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_functions

    Even functions are those real functions whose graph is self-symmetric with respect to the y-axis, and odd functions are those whose graph is self-symmetric with respect to the origin. If the domain of a real function is self-symmetric with respect to the origin, then the function can be uniquely decomposed as the sum of an even function and an ...

  7. Symmetry (geometry) - Wikipedia

    en.wikipedia.org/wiki/Symmetry_(geometry)

    The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical. Another way to think about it is that if the shape were to be folded in half over the axis, the two halves would be identical as mirror ...

  8. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    Graph of y = ax 2 + bx + c, where a and the discriminant b 2 − 4ac are positive, with. Roots and y-intercept in red; Vertex and axis of symmetry in blue; Focus and directrix in pink; Visualisation of the complex roots of y = ax 2 + bx + c: the parabola is rotated 180° about its vertex (orange).

  9. Rotational symmetry - Wikipedia

    en.wikipedia.org/wiki/Rotational_symmetry

    Rotational symmetry of order n, also called n-fold rotational symmetry, or discrete rotational symmetry of the n th order, with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of ⁠ ⁠ (180°, 120°, 90°, 72°, 60°, 51 3 ⁄ 7 °, etc.) does not change the object. A "1-fold" symmetry is no symmetry (all ...