Maple

> with(linalg);
> Y := matrix([[2], [5], [1], [7]]);

> L := matrix([[1, 1, 1, 1], [1, -1, 1, -1], [1, 0, 0, 0], [1, -2, 4, -8]]);

> L1 := matrix([[1, 1, 1, 1], [1, -1, 0, -2], [1, 1, 0, 4],[1, -1, 0, -8]]);

> M := evalm(`&*`(L1, L));

> B := inverse(M);

> T := evalm(`&*`(L1, Y));

> R := evalm(`&*`(B, T));

> with(plottools);
> with(plots);
> E := pointplot({[-2, 7], [-1,5], [0, 1], [1, 2]}, color = red, symbol = CIRCLE, symbolsize = 10);
PLOT(POINTS([-2., 7.], [-1., 5.], [0., 1.], [1., 2.]),

COLOUR(RGB, 1.00000000, 0., 0.), SYMBOL(CIRCLE, 10))
> H :=plot(1-(8/3)*x+(5/2)*x^2+(7/6)*x^3, x = -2 .. 2);
PLOT(CURVES([[-2., 7.00000000000000],

[-1.97896957989950, 7.02606115809226],

[-1.96067112381910, 7.04554905039473],[-1.94009259618090, 7.06397733686766],

[-1.91937766070352, 7.07885800768446],

[-1.89876117969849, 7.09007381415494],

[-1.87964706271357, 7.09732269064566],[-1.85985550170854, 7.10168842539986],

[-1.83938704100503, 7.10290005877004],

[-1.81898422291457, 7.10082400783514],

[-1.79799741668342, 7.09533059286102],[-1.77951222633166, 7.08772231456926],

[-1.75870228020101, 7.07611067744004],

[-1.73780688643216, 7.06126590165940],

[-1.71767030271357, 7.04399960481112],[-1.69938435557789, 7.02585123994269],

[-1.67764059577889, 7.00127359818984],

[-1.65922077909548, 6.97795580878508],

[-1.63779415336683, 6.94801100524718],[-1.61882795899498, 6.91902633793916],

[-1.59801903778894, 6.88460700184083],

[-1.57820402391960, 6.84934091422431],

[-1.55752913567839, 6.81001406700745],

[-1.53854313427136,6.77167588798483],

[-1.51806416683417, 6.72799280813070],

[-1.49679227517588, 6.68012070633058],

[-1.47827503095477, 6.63642764589904],

[-1.45827589989950,...