DescriptionLagrange polynomial.svg	English:   This W3C-unspecified diagram was created with Mathematica. This image shows, for four points ((−9, 5), (−4, 2), (−1, −2), (7, 9)), the (cubic) interpolation polynomial L(x) (dashed, black), which is the sum of the scaled basis polynomials y1ℓ1(x), y2ℓ2(x), y3ℓ3(x) and y4ℓ4(x) (colors). The interpolation polynomial passes through all four control points, and each scaled basis polynomial passes through its respective control point and is 0 where x corresponds to the other three control points.
Date	26 December 2015
Source	Self-made, based on Image:Lagrangepolys.png
Author	User:Glosser.ca
Other versions	Image:Lagrangepolys.png

colors = ColorData[97] /@ Range[4];
pts = {{\[Minus]9, 5}, {\[Minus]4, 2}, {\[Minus]1, \[Minus]2}, {7, 9}};
{xs, ys} = Transpose[pts];

Basis[pts_, x_] := Times @@ (x - DeleteCases[pts, #])/Times @@ (# - DeleteCases[pts, #]) & /@ pts

Plot[
 {
  Evaluate[ys*Basis[xs, x]],
  Total[ys*Basis[xs, x]]
 }, {x, -9, 7},
 PlotStyle -> {Automatic, Automatic, Automatic, Automatic, Directive[Black, Dashed]},
 Frame -> True,
 Axes -> False,
 ImageSize -> Large,
 GridLines -> Automatic,
 GridLinesStyle -> Directive[LightGray, Dashed],
 PlotStyle -> Thick,
 Epilog -> Table[{PointSize[0.02], ColorData[97][i], Point[pts[[i]]]}, {i,4}],
 PlotLegends -> Placed[
  LineLegend[{
   Subscript[\[ScriptL], 1][x], 
   Subscript[\[ScriptL], 2][x],
   Subscript[\[ScriptL], 3][x], 
   Subscript[\[ScriptL], 4][x],
   L[x]
  }, LegendLayout -> {"Row", 1}],
  Top
 ],
 FrameStyle -> Black
]

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