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Polynomial functions

Degree, end behaviour, zeros, turning points, and what the graph must look like.

A polynomial of degree n has at most n real zeros and at most n − 1 turning points, and its ends point where the leading term sends them. Factoring finds the zeros; the derivative finds the turning points. Type a polynomial as y = … to see all of it at once.

דוגמה עובדת: y = x^3 - 3x

Algebra · Functions

Graph and analyse x^3 - 3x

y = x^{3} - 3 x

צעד אחר צעד

  1. x^{3} - 3 x

    An expression in x. Here is what it does.

  2. x \left(x^{2} - 3\right)

    Simplified form.

  3. x = 0, x = - \sqrt{3}, x = \sqrt{3}

    Real zeros (where the graph crosses the axis).

  4. \frac{d}{dx} = 3 x^{2} - 3

    Derivative (slope).

גלה את התשובה
x \left(x^{2} - 3\right)

נסה את שלך.

יותר בפנים. Precalculus

Complex numbersRational functionsSequences and seriesThe binomial theoremConic sectionsVectors