Cubic function

A polynomial function of degree three, usually written as f(x) = ax³ + bx² + cx + d with a ≠ 0. Its graph has opposite end behavior on the two sides of the real line.

Polynomial root: A value that makes a polynomial equal zero. Roots determine where a cubic function crosses or touches the x-axis.
Polynomial: An algebraic expression formed from sums of terms with nonnegative integer powers of variables. Cubic functions are formed by evaluating a polynomial at each input.
Quadratic function: A polynomial function of degree two, with a graph that is a parabola. Unlike a quadratic, a cubic can have two turning points and opposite end behavior.
Cubic spline: A piecewise function made of cubic polynomials joined with specified smoothness conditions. Cubic pieces provide flexible curves while maintaining smooth joins.
Derivative: A function that gives the instantaneous rate of change of another function. The derivative of a cubic is quadratic and locates its stationary points.
Leading coefficient: The coefficient of the term with the highest degree in a polynomial. Its sign determines which direction each end of a cubic graph faces.
Quartic function: A polynomial function of degree four. A quartic has the same end behavior at both extremes, unlike a cubic.
Cubic interpolation: A method for estimating values between data points using cubic polynomials. Cubic curves can fit data while controlling slope and curvature.
Inflection point: A point where a curve changes its direction of concavity. Every cubic function has exactly one real inflection point.
Factor theorem: A theorem stating that x − r divides a polynomial exactly when r is one of its roots. It turns a known cubic root into a linear factor.

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