What is cubic parabola

Determine polynomial function (cubic parabola made of points)

n = degree of the polynomial (3) general equation of a polynomial fo (x) = an xn + ... + a1 x + a0 , (is adjusted when entering) Cubic parabola n = 3 through (-1.2), (2, -1) (-3.34) with local maximum at x = 1 input boxes Insertion of the points described in the general function equation fo GLS : {{- 1, 2}, {2, -1}, {-3, 34}, {1, 0, 1}} Entry is transferred to the CAS: A point (x, y) of the parabola y = f ( x) is entered as {x, y}, the kth derivative f (x) dx = y as {x, y, k} e.g. 1st derivative f '(2) = 0 as {2,0,1} The system of equations resulting from the information is in line (5) and transferred to a matrix in line (8). Solution with inverse matrix (9) or using the Gaussian algorithm from line (12). Matrix templates are only for cubic parabolas R4 - n = 3 designed! alternatively (4) →: Shows the direct entry of the task in the CAS: if necessary, overwrite line (4) with it. (4) GLS: = {fo (-1) = 2, fo (2) = -1, fo (-3) = 34, fo '(1) = 0} from this I get a linear system of equations GLS (5). The input box GLS places the information in the algebra window and the information may lose its accuracy (√2 ~ 1.4142). If you want to avoid this, the information must be given directly in CAS line 4 in the form (4) → shown. If the online app does not calculate line (3) independently - does the line have to be calculated manually?