Quartic function
![Graph of a polynomial of degree 4, with 3 critical points and four real roots (crossings of the x axis) (and thus no complex roots). If one or the other of the local minima were above the x axis, or if the local maximum were below it, or if there were no local maximum and one minimum below the x axis, there would only be two real roots (and two complex roots). If all three local extrema were above the x axis, or if there were no local maximum and one minimum above the x axis, there would be no real root (and four complex roots).](/Images/godic/202412/24/Polynomialdeg4.svg2205.png")
- This article is about the univariate quartic. For the bivariate quartic, see Quartic plane curve.
In algebra, a quartic function is a function of the form
where a is nonzero, which is defined by a polynomial of degree four, called quartic polynomial.
Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form