It can be written as:
f(x) = a4 x4 + a3 x3 + a2 x2 +a1 x + a0.
- a4 is a nonzero constant.
- a3, a2, a1 and a0 are also constants, but they may be equal to zero.
The quartic was first solved by mathematician Lodovico Ferrari in 1540.
Graph of a Quartic Function
The graph of a fourth-degree polynomial will often look roughly like an M or a W, depending on whether the highest order term is positive or negative.
- If the coefficient of the leading term, a, is positive, the function will go to infinity at both sides.
- If the coefficient a is negative the function will go to minus infinity on both sides.
The image below shows the graph of one quartic function. This particular function has a positive leading term, and four real roots.
Three basic shapes are possible. For a > 0:
Properties of Quartic Polynomials
Fourth degree polynomials all share a number of properties:
- They have up to four roots,
- Their derivatives have from 1 to 3 roots,
- They have no general symmetry,
- They can have one, two, or no (zero) inflection points,
- Five points, or five pieces of information, can describe it completely,
- Every polynomial equation can be solved by radicals.
Davidson, Jon. Fourth Degree Polynomials. Retrieved from https://www.sscc.edu/home/jdavidso/math/catalog/polynomials/fourth/fourth.html on May 16, 2019.
Stephanie Glen. "Quartic Function: Definition, Example" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/types-of-functions/quartic-function/
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