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  2. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    () = + is called the vertex form, where h and k are the x and y coordinates of the vertex, respectively. The coefficient a is the same value in all three forms. To convert the standard form to factored form , one needs only the quadratic formula to determine the two roots r 1 and r 2 .

  3. 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 2y 2. Generalizations to more variables yield ...

  4. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    Quadratic formula. The roots of the quadratic function y = ⁠ 1 2 ⁠x2 − 3x + ⁠ 5 2 ⁠ are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.

  5. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Quadratic equation. In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [ 1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)

  6. Simplex - Wikipedia

    en.wikipedia.org/wiki/Simplex

    Simplex. The four simplexes that can be fully represented in 3D space. In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension.

  7. YΔ- and ΔY-transformation - Wikipedia

    en.wikipedia.org/wiki/YΔ-_and_ΔY-transformation

    In graph theory, ΔY- and YΔ-transformations (also written delta-wye and wye-delta) are a pair of operations on graphs. A ΔY-transformation replaces a triangle by a vertex of degree three; and conversely, a YΔ-transformation replaces a vertex of degree three by a triangle. The names for the operations derive from the shapes of the involved ...

  8. Homogeneous coordinates - Wikipedia

    en.wikipedia.org/wiki/Homogeneous_coordinates

    In particular, (x, y, 1) is such a system of homogeneous coordinates for the point (x, y). For example, the Cartesian point (1, 2) can be represented in homogeneous coordinates as (1, 2, 1) or (2, 4, 2). The original Cartesian coordinates are recovered by dividing the first two positions by the third.

  9. Vertex (curve) - Wikipedia

    en.wikipedia.org/wiki/Vertex_(curve)

    Vertex (curve) An ellipse (red) and its (blue). The dots are the vertices of the curve, each corresponding to a cusp on the evolute. In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero. [1] This is typically a local maximum or minimum of curvature, [2] and some authors define a vertex to be ...