Cubic Equation

cubic_equation(first_constant, second_constant, third_constant, fourth_constant, precision=4)

Generates a cubic function to provide evaluations at variable inputs

Parameters

  • first_constant (int or float) – Coefficient of the cubic term of the resultant cubic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • second_constant (int or float) – Coefficient of the quadratic term of the resultant cubic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • third_constant (int or float) – Coefficient of the linear term of the resultant cubic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • fourth_constant (int or float) – Coefficient of the constant term of the resultant cubic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

  • precision (int, default=4) – Maximum number of digits that can appear after the decimal place of the resultant roots

Raises

  • TypeError – First four arguments must be integers or floats

  • ValueError – Last argument must be a positive integer

Returns

evaluation – Function for evaluating a cubic equation when passed any integer or float argument

Return type

func

See also

cubic_derivatives(), cubic_integral(), cubic_roots(), cubic_model()

Notes

  • Standard form of a cubic function: \(f(x) = a\cdot{x^3} + b\cdot{x^2} + c\cdot{x} + d\)

  • Cubic Functions

Examples

Import cubic_equation function from regressions library
>>> from regressions.analyses.equations.cubic import cubic_equation
Create a cubic function with coefficients 2, 3, 5, and 7, then evaluate it at 10
>>> evaluation_first = cubic_equation(2, 3, 5, 7)
>>> print(evaluation_first(10))
2357.0
Create a cubic function with coefficients 7, -5, -3, and 2, then evaluate it at 10
>>> evaluation_second = cubic_equation(7, -5, -3, 2)
>>> print(evaluation_second(10))
6472.0
Create a cubic function with all inputs set to 0, then evaluate it at 10
>>> evaluation_zero = cubic_equation(0, 0, 0, 0)
>>> print(evaluation_zero(10))
0.1111