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The same reasoning applies in reverse to polynomial with a negative quartic coefficient. In algebra, a quartic function is a function of the form = + + + +, α. where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
Graph of a polynomial function of degree 4, with its 4 roots and 3 critical points. + + + + = where a ≠ 0. The quartic is the highest order polynomial equation that can be solved by radicals in the general case (i.e., one in which the coefficients can take any value).
For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x ...
Polynomial curves fitting points generated with a sine function. The black dotted line is the "true" data, the red line is a first degree polynomial, the green line is second degree, the orange line is third degree and the blue line is fourth degree. The first degree polynomial equation = + is a line with slope a. A line will connect any two ...
Polynomials of degree one, two or three are respectively linear polynomials, quadratic polynomials and cubic polynomials. [8] For higher degrees, the specific names are not commonly used, although quartic polynomial (for degree four) and quintic polynomial (for degree five) are sometimes used. The names for the degrees may be applied to the ...
The cruciform curve, or cross curve is a quartic plane curve given by the equation = where a and b are two parameters determining the shape of the curve. The cruciform curve is related by a standard quadratic transformation, x ↦ 1/x, y ↦ 1/y to the ellipse a 2 x 2 + b 2 y 2 = 1, and is therefore a rational plane algebraic curve of genus zero.
With the advent of computer graphics, Bernstein polynomials, restricted to the interval [0, 1], became important in the form of Bézier curves. A numerically stable way to evaluate polynomials in Bernstein form is de Casteljau's algorithm. Bernstein basis polynomials for 4th degree curve blending
The graph below shows an example of this, producing a fourth-degree polynomial approximating over [−1, 1]. The test points were set at −1, −0.7, −0.1, +0.4, +0.9, and 1. Those values are shown in green. The resultant value of is 4.43 × 10 −4