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  2. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form ⁠ + + ⁠ to the form ⁠ + ⁠ for some values of ⁠ ⁠ and ⁠ ⁠. [1] In terms of a new quantity ⁠ x − h {\displaystyle x-h} ⁠ , this expression is a quadratic polynomial with no linear term.

  3. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    To complete the square, form a squared binomial on the left-hand side of a quadratic equation, from which the solution can be found by taking the square root of both sides. The standard way to derive the quadratic formula is to apply the method of completing the square to the generic quadratic equation ⁠ a x 2 + b x + c = 0 {\displaystyle ...

  4. Quadratic form - Wikipedia

    en.wikipedia.org/wiki/Quadratic_form

    A mapping q : M → R : v ↦ b(v, v) is the associated quadratic form of b, and B : M × M → R : (u, v) ↦ q(u + v) − q(u) − q(v) is the polar form of q. A quadratic form q : M → R may be characterized in the following equivalent ways: There exists an R-bilinear form b : M × M → R such that q(v) is the associated quadratic form.

  5. 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 ...

  6. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Abū Kāmil Shujā ibn Aslam (Egypt, 10th century) in particular was the first to accept irrational numbers (often in the form of a square root, cube root or fourth root) as solutions to quadratic equations or as coefficients in an equation. [30] The 9th century Indian mathematician Sridhara wrote down rules for solving quadratic equations. [31]

  7. Parent function - Wikipedia

    en.wikipedia.org/wiki/Parent_function

    For example, for the family of quadratic functions having the general form = + +, the simplest function is =, and every quadratic may be converted to that form by translations and dilations, which may be seen by completing the square. This is therefore the parent function of the family of quadratic equations.

  8. Golfer Grayson Murray Told His Father He 'Didn't Want to Be ...

    www.aol.com/golfer-grayson-murray-told-father...

    The father of late pro golfer Grayson Murray is opening up about a conversation he had with his son shortly before his tragic death. In a new interview with Golf Digest, Murray’s family shared ...

  9. 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.