w1 = [-5,5];
w2 = [-3,1];
w3 = [1,2];
X = zeros(3,3);
X(1,1) = ((w1(1) - 0) * (w1(1) - w2(1)) * (w1(1) - w3(1)));
X(2,2) = ((w2(1) - 0) * (w2(1) - w1(1)) * (w2(1) - w3(1)));
X(3,3) = ((w3(1) - 0) * (w3(1) - w1(1)) * (w3(1) - w2(1)));
Y = zeros(3,1);
Y(1,1) = w1(2);
Y(2,1) = w2(2);
Y(3,1) = w3(2);
display(X);
display(Y);
A = inv(X) * Y;
display(A);
fprintf(' W(x)=%f*x^3 + %f*x^2 + %f*x\n', A(3,1), A(2,1), A(1,1));
x=[-5:1:5];
y=zeros(1,11);
for i=1:11
 y(i)=A(1,1)+A(2,1)*x(i)+A(3,1)*x(i)^2;
end
plot(x, y);
grid on;
hold on;
vector_x=[w1(1,1), w2(1,1), w3(1,1)];
vector_y=zeros(1, 3);
for i=1:3
 vector_y(1,1)=vector_y(1,1)+A(i,1)*w1(1,1)^(i-1);
 vector_y(1,2)=vector_y(1,2)+A(i,1)*w2(1,1)^(i-1);
 vector_y(1,3)=vector_y(1,3)+A(i,1)*w3(1,1)^(i-1);
end
plot(vector_x,vector_y,'rx');
plot(w1(1,1),w1(1,2),'--gs');
plot(w2(1,1),w2(1,2),'--gs');
plot(w3(1,1),w3(1,2),'--gs');
title("Interpolacja Lagrange’a – Z2a");
ylabel('Os y');
xlabel('Os x');