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  2. Parabola - Wikipedia

    en.wikipedia.org/wiki/Parabola

    In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...

  3. List of types of functions - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_functions

    Continuous function: in which preimages of open sets are open.; Nowhere continuous function: is not continuous at any point of its domain; for example, the Dirichlet function.

  4. Quadrature of the Parabola - Wikipedia

    en.wikipedia.org/wiki/Quadrature_of_the_Parabola

    A parabolic segment is the region bounded by a parabola and line. To find the area of a parabolic segment, Archimedes considers a certain inscribed triangle. The base of this triangle is the given chord of the parabola, and the third vertex is the point on the parabola such that the tangent to the parabola at that point is parallel to the chord.

  5. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    Given a quadratic polynomial of the form + the numbers h and k may be interpreted as the Cartesian coordinates of the vertex (or stationary point) of the parabola. That is, h is the x -coordinate of the axis of symmetry (i.e. the axis of symmetry has equation x = h ), and k is the minimum value (or maximum value, if a < 0) of the quadratic ...

  6. Eccentricity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Eccentricity_(mathematics)

    A family of conic sections of varying eccentricity share a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated ...

  7. Superparabola - Wikipedia

    en.wikipedia.org/wiki/Superparabola

    Superparabola functions. A superparabola is a geometric curve defined in the Cartesian coordinate system as a set of points (x, y) with = [()], where p, a, and b are positive integers.

  8. Semicubical parabola - Wikipedia

    en.wikipedia.org/wiki/Semicubical_parabola

    In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve that has an implicit equation of the form y 2 − a 2 x 3 = 0 {\displaystyle y^{2}-a^{2}x^{3}=0} (with a ≠ 0 ) in some Cartesian coordinate system .

  9. Paraboloid - Wikipedia

    en.wikipedia.org/wiki/Paraboloid

    In this position, the hyperbolic paraboloid opens downward along the x-axis and upward along the y-axis (that is, the parabola in the plane x = 0 opens upward and the parabola in the plane y = 0 opens downward). Any paraboloid (elliptic or hyperbolic) is a translation surface, as it can be generated by a moving parabola directed by a second ...

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