Cubic function
（重定向自Cubic functions）
![Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis—where y = 0). The case shown has two critical points. Here the function is ƒ(x) = (x3 + 3x2 − 6x − 8) / 4.](/Images/godic/202501/07/Polynomialdeg3.svg4920.png")
![Two-dimensional graph of a cubic, the polynomial ƒ(x) = 2x3 − 3x2 − 3x + 2.](/Images/godic/202501/07/Graph_of_cubic_polynomial.svg4920.png")
![Niccolò Fontana Tartaglia](/Images/godic/202501/07/Niccolò_Tartaglia4920.jpg")
![The roots, turning points, stationary points, inflection point and concavity of a cubic polynomial x³ - 3x² - 144x + 432 (black line) and its first and second derivatives (red and blue).](/Images/godic/202501/07/Cubic_graph_special_points.svg4921.png")
In algebra, a cubic function is a function of the form
where a is nonzero. In other words, a cubic function is defined by a polynomial of degree three.
Setting ƒ(x) = 0 produces a cubic equation of the form:
Usually, the coefficients a, b, c, d are real numbers. However much of the theory of cubic equations for real coefficients applies to other types of coefficients (such as complex ones).