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  2. Envelope (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Envelope_(mathematics)

    The same idea underlies the solution of a first order equation as an integral of the Monge cone. [5] The Monge cone is a cone field in the R n+1 of the (x,u) variables cut out by the envelope of the tangent spaces to the first order PDE at each point. A solution of the PDE is then an envelope of the cone field.

  3. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    The roots of the quadratic function y = ⁠ 1 / 2x 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.

  4. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    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 function f(x − h) = (x − h) 2 is a parabola shifted to the right by h whose vertex is at (h, 0), as shown in the top figure.

  5. Today’s NYT ‘Strands’ Hints, Spangram and Answers for ...

    www.aol.com/today-nyt-strands-hints-spangram...

    We'll cover exactly how to play Strands, hints for today's spangram and all of the answers for Strands #283 on Wednesday, December 11. Related: 16 Games Like Wordle To Give You Your Word Game Fix ...

  6. Why are Americans obsessed with a white Christmas? Blame ...

    www.aol.com/why-americans-obsessed-white...

    Americans are obsessed with a white Christmas and all the trimmings – snow, icicles, sleigh rides, frost on windowpanes, cuddling up by the fire, mittens, the North Pole. Christmas is a ...

  7. Square (algebra) - Wikipedia

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

    For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 + 2x + 1. One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that (for all numbers x), the square of x is the same as the square of its additive inverse −x.

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