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  2. 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 ...

  3. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    To convert the standard form to factored form, one needs only the quadratic formula to determine the two roots r 1 and r 2. To convert the standard form to vertex form, one needs a process called completing the square. To convert the factored form (or vertex form) to standard form, one needs to multiply, expand and/or distribute the factors.

  4. Solving quadratic equations with continued fractions - Wikipedia

    en.wikipedia.org/wiki/Solving_quadratic...

    The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated ...

  5. 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.)

  6. 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.

  7. Convex hull algorithms - Wikipedia

    en.wikipedia.org/wiki/Convex_hull_algorithms

    Insertion of a point may increase the number of vertices of a convex hull at most by 1, while deletion may convert an n-vertex convex hull into an n-1-vertex one. The online version may be handled with O(log n) per point, which is asymptotically optimal. The dynamic version may be handled with O(log 2 n) per operation. [1]

  8. How a GM layoff email sent to employees triggered a storm on ...

    www.aol.com/gm-layoff-email-sent-employees...

    The Detroit Free Press reported at the time that 634 of the jobs being cut then were at the GM Global Technical Center in Warren based on information provided to the state of Michigan.

  9. Quadratic form - Wikipedia

    en.wikipedia.org/wiki/Quadratic_form

    The notion of a quadratic space is a coordinate-free version of the notion of quadratic form. Sometimes, Q is also called a quadratic form. Two n -dimensional quadratic spaces ( V , Q ) and ( V ′, Q ′) are isometric if there exists an invertible linear transformation T : V → V ′ ( isometry ) such that Q ( v ) = Q ′ ( T v ) for all v ...