Cubic function | cubic equation formula
Polynomialfunctionofdegree3Graphofacubicfunctionwith3realroots(wherethecurvecrossesthehorizontalaxis—wherey=0).Thecaseshownhastwocriticalpoints.Herethefunctionisf(x)=(x3+3x2−6x−8)/4.Inmathematics,acubicfunctionisafunctionoftheformf(x)=ax3+bx2+cx+d{displaystylef(x)=ax{3}+bx{2}+cx+d}wherethecoefficientsa,b,c,anddarecomplexnumbers,andthevariablextakesrealvalues,anda≠0{displaystyleaeq0}.Inotherwords,itisbothapolynomialfunctionofdegreethree,andarealfunction.Inparticular,thedomainandthecodomainare...
Polynomial function of degree 3
Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis—where y = 0). The case shown has two critical points. Here the function is f(x) = (x3 + 3x2 − 6x − 8)/4.In mathematics, a cubic function is a function of the form f(x)=ax3+bx2+cx+d{displaystyle f(x)=ax{3}+bx{2}+cx+d} where the coefficients a, b, c, and d are complex numbers, and the variable x takes real values, and a≠0{displaystyle a eq 0}. In other words, it is both a polynomial function of degree three, and a real function. In particular, the domain and the codomain are the set of the real numbers.
Setting f(x) = 0 produces a cubic equation of the form
ax3+bx2+cx+d=0,{displaystyle ax{3}+bx{2}+cx+d=0,}whose solutions are called roots of the function.
A cubic function has either one or three real roots (which may not be distinct);[1] all odd-degree polynomials have at least one real root.
The graph of a cubic function...