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  2. 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.

  3. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    Given a general quadratic equation of the form ⁠ + + = ⁠, with ⁠ ⁠ representing an unknown, and coefficients ⁠ ⁠, ⁠ ⁠, and ⁠ ⁠ representing known real or complex numbers with ⁠ ⁠, the values of ⁠ ⁠ satisfying the equation, called the roots or zeros, can be found using the quadratic formula,

  4. 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.

  5. 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 ...

  6. Factorization of polynomials - Wikipedia

    en.wikipedia.org/wiki/Factorization_of_polynomials

    If two or more factors of a polynomial are identical, then the polynomial is a multiple of the square of this factor. The multiple factor is also a factor of the polynomial's derivative (with respect to any of the variables, if several). For univariate polynomials, multiple factors are equivalent to multiple roots (over a suitable extension field).

  7. 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 − 4x + 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. This is because ...

  8. Thomas H. Kean - Pay Pals - The Huffington Post

    data.huffingtonpost.com/paypals/thomas-h-kean

    From January 2008 to December 2012, if you bought shares in companies when Thomas H. Kean joined the board, and sold them when he left, you would have a -67.6 percent return on your investment, compared to a -2.8 percent return from the S&P 500.

  9. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    All quadratic equations have exactly two solutions in complex numbers (but they may be equal to each other), a category that includes real numbers, imaginary numbers, and sums of real and imaginary numbers. Complex numbers first arise in the teaching of quadratic equations and the quadratic formula. For example, the quadratic equation

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