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  2. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    The square root of a univariate quadratic function gives rise to one of the four conic sections, almost always either to an ellipse or to a hyperbola. If a > 0 , {\displaystyle a>0,} then the equation y = ± a x 2 + b x + c {\displaystyle y=\pm {\sqrt {ax^{2}+bx+c}}} describes a hyperbola, as can be seen by squaring both sides.

  3. 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.

  4. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    The function f(x) = ax 2 + bx + c is a quadratic function. [16] The graph of any quadratic function has the same general shape, which is called a parabola. The location and size of the parabola, and how it opens, depend on the values of a, b, and c. If a > 0, the parabola has a minimum point and opens upward.

  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. Conjugate (square roots) - Wikipedia

    en.wikipedia.org/wiki/Conjugate_(square_roots)

    In mathematics, the conjugate of an expression of the form + is , provided that does not appear in a and b.One says also that the two expressions are conjugate. In particular, the two solutions of a quadratic equation are conjugate, as per the in the quadratic formula =.

  7. Square (algebra) - Wikipedia

    en.wikipedia.org/wiki/Square_(algebra)

    On the negative numbers, numbers with greater absolute value have greater squares, so the square is a monotonically decreasing function on (−∞,0]. Hence, zero is the (global) minimum of the square function. The square x 2 of a number x is less than x (that is x 2 < x) if and only if 0 < x < 1, that is, if x belongs to the open interval (0,1).

  8. Parent function - Wikipedia

    en.wikipedia.org/wiki/Parent_function

    For linear and quadratic functions, the graph of any function can be obtained from the graph of the parent function by simple translations and stretches parallel to the axes. For example, the graph of y = x 2 − 4 x + 7 can be obtained from the graph of y = x 2 by translating +2 units along the X axis and +3 units along Y axis.

  9. Quadratic programming - Wikipedia

    en.wikipedia.org/wiki/Quadratic_programming

    The quadratic programming problem with n variables and m constraints can be formulated as follows. [2] Given: a real-valued, n-dimensional vector c, an n×n-dimensional real symmetric matrix Q, an m×n-dimensional real matrix A, and; an m-dimensional real vector b, the objective of quadratic programming is to find an n-dimensional vector x ...

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