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  2. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    In mathematics, a quadratic function of a single variable is a function of the form [1] = + +,,where ⁠ ⁠ is its variable, and ⁠ ⁠, ⁠ ⁠, and ⁠ ⁠ are coefficients.The expression ⁠ + + ⁠, especially when treated as an object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two.

  3. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

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

  4. 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 ...

  5. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    The roots of the quadratic function y = ⁠ 1 / 2 ⁠ x 2 − 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.

  6. Graph of a function - Wikipedia

    en.wikipedia.org/wiki/Graph_of_a_function

    Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.

  7. Quadratic form - Wikipedia

    en.wikipedia.org/wiki/Quadratic_form

    In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, 4 x 2 + 2 x y − 3 y 2 {\displaystyle 4x^{2}+2xy-3y^{2}}

  8. Definite quadratic form - Wikipedia

    en.wikipedia.org/wiki/Definite_quadratic_form

    In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative) for every non-zero vector of V. According to that sign, the quadratic form is called positive-definite or negative-definite .

  9. Y-intercept - Wikipedia

    en.wikipedia.org/wiki/Y-intercept

    Graph = with the -axis as the horizontal axis and the -axis as the vertical axis.The -intercept of () is indicated by the red dot at (=, =).. In analytic geometry, using the common convention that the horizontal axis represents a variable and the vertical axis represents a variable , a -intercept or vertical intercept is a point where the graph of a function or relation intersects the -axis of ...

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