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  2. 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). Therefore, the graph of the ...

  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. Resolution of singularities - Wikipedia

    en.wikipedia.org/wiki/Resolution_of_singularities

    The transform of the ideal in the x-chart if generated by x-y 2 and y 2 (y 2 +z 2-w 3). The next center of blowing up C 1 is given by x=y=0. However, the strict transform of X is X 1, which is generated by x-y 2 and y 2 +z 2-w 3. This means that the intersection of C 1 and X 1 is given by x=y=0 and z 2-w 3 =0, which is not regular.

  5. Sylvester's law of inertia - Wikipedia

    en.wikipedia.org/wiki/Sylvester's_law_of_inertia

    If is the coefficient matrix of some quadratic form of ⁠ ⁠, then is the matrix for the same form after the change of basis defined by ⁠ ⁠. A symmetric matrix A {\displaystyle A} can always be transformed in this way into a diagonal matrix D {\displaystyle D} which has only entries ⁠ 0 {\displaystyle 0} ⁠ , ⁠ + 1 {\displaystyle +1 ...

  6. Wikipedia:Reference desk/Archives/Mathematics/2009 February 8 ...

    en.wikipedia.org/wiki/Wikipedia:Reference_desk/...

    The formula for finding roots to these equations are a lot simpler than the quadratic formula; x=(±t-k)/s, and for quadratic functions with a non unit coefficient for x 2, my method is simpler than factorizing.The Successor of Physics 10:07, 11 February 2009 (UTC)

  7. 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.

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    The AOL.com video experience serves up the best video content from AOL and around the web, curating informative and entertaining snackable videos.

  9. Principal axis theorem - Wikipedia

    en.wikipedia.org/wiki/Principal_axis_theorem

    The trick is to write the quadratic form as + + = [] [] [] = where the cross-term has been split into two equal parts. The matrix A in the above decomposition is a symmetric matrix . In particular, by the spectral theorem , it has real eigenvalues and is diagonalizable by an orthogonal matrix ( orthogonally diagonalizable ).

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