Quadratic Roots

quadratic_roots(first_constant, second_constant, third_constant, precision=4)

Calculates the roots of a quadratic function

Parameters

  • first_constant (int or float) – Coefficient of the quadratic term of the original quadratic 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 linear term of the original quadratic 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 constant term of the original quadratic 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 three arguments must be integers or floats

  • ValueError – Last argument must be a positive integer

Returns

roots – List of the x-coordinates of all of the x-intercepts of the original function; if the function never crosses the x-axis, then it will return a list of None

Return type

list of float

See also

quadratic_equation(), quadratic_derivatives(), quadratic_integral(), quadratic_model()

Notes

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

  • Quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

  • Quadratic Formula

Examples

Import quadratic_roots function from regressions library
>>> from regressions.analyses.roots.quadratic import quadratic_roots
Calculate the roots of a quadratic function with coefficients 2, 7, and 5
>>> roots_first = quadratic_roots(2, 7, 5)
>>> print(roots_first)
[-2.5, -1.0]
Calculate the roots of a quadratic function with coefficients 2, -5, and 3
>>> roots_second = quadratic_roots(2, -5, 3)
>>> print(roots_second)
[1.0, 1.5]
Calculate the roots of a quadratic function with all inputs set to 0
>>> roots_zeroes = quadratic_roots(0, 0, 0)
>>> print(roots_zeroes)
[None]