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  2. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    The quadratic formula can equivalently be written using various alternative expressions, for instance = (), which can be derived by first dividing a quadratic equation by ⁠ ⁠, resulting in ⁠ + + = ⁠, then substituting the new coefficients into the standard quadratic formula.

  3. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.

  4. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    If a quadratic function is equated with zero, then the result is a quadratic equation. The solutions of a quadratic equation are the zeros (or roots) of the corresponding quadratic function, of which there can be two, one, or zero. The solutions are described by the quadratic formula. A quadratic polynomial or quadratic function can involve ...

  5. Curve fitting - Wikipedia

    en.wikipedia.org/wiki/Curve_fitting

    The first degree polynomial equation = + is a line with slope a. A line will connect any two points, so a first degree polynomial equation is an exact fit through any two points with distinct x coordinates. If the order of the equation is increased to a second degree polynomial, the following results:

  6. 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 ...

  7. Vieta jumping - Wikipedia

    en.wikipedia.org/wiki/Vieta_jumping

    We know that one root of this equation is x 1 = A. By standard properties of quadratic equations, we know that the other root satisfies x 2 = kB – A and x 2 = ⁠ B 2 – k / A ⁠. The first expression for x 2 shows that x 2 is an integer, while the second expression implies that x 2 ≠ 0 since k is not a perfect square.

  8. Linearization - Wikipedia

    en.wikipedia.org/wiki/Linearization

    Linearizations of a function are lines—usually lines that can be used for purposes of calculation. Linearization is an effective method for approximating the output of a function = at any = based on the value and slope of the function at =, given that () is differentiable on [,] (or [,]) and that is close to .

  9. Slope - Wikipedia

    en.wikipedia.org/wiki/Slope

    Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.