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  2. 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.

  3. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    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 more than one variable.

  4. 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.

  5. Zero of a function - Wikipedia

    en.wikipedia.org/wiki/Zero_of_a_function

    It follows that the solutions of such an equation are exactly the zeros of the function . In other words, a "zero of a function" is precisely a "solution of the equation obtained by equating the function to 0", and the study of zeros of functions is exactly the same as the study of solutions of equations.

  6. Hurwitz polynomial - Wikipedia

    en.wikipedia.org/wiki/Hurwitz_polynomial

    A polynomial function P(s) of a complex variable s is said to be Hurwitz if the following conditions are satisfied: P(s) is real when s is real. The roots of P(s) have real parts which are zero or negative. Hurwitz polynomials are important in control systems theory, because they represent the characteristic equations of stable linear systems.

  7. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    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 function. One way to see this is to note that the graph of the function f ( x ) = x 2 is a parabola whose vertex is at the origin (0, 0).

  8. Discriminant - Wikipedia

    en.wikipedia.org/wiki/Discriminant

    A quadratic form in four variables is the equation of a projective surface. The surface has a singular point if and only its discriminant is zero. In this case, either the surface may be decomposed in planes, or it has a unique singular point, and is a cone or a cylinder .

  9. Degree of a polynomial - Wikipedia

    en.wikipedia.org/wiki/Degree_of_a_polynomial

    For example, a degree two polynomial in two variables, such as + +, is called a "binary quadratic": binary due to two variables, quadratic due to degree two. [ a ] There are also names for the number of terms, which are also based on Latin distributive numbers, ending in -nomial ; the common ones are monomial , binomial , and (less commonly ...