1. Make a MATLAB program that graphs the second order interpolating polynomial using Lagrange's formula. The inputs of the function should be a, b, x, y where a and b are numbers and z and y are vectors, each of length 3. The variables a and b indicate the interval over which the function will be graphed, and the vectors z and y contain the z and y coordinates of the points through which the polynomial passes. Note that MATLAB does not allow zero indices. 2. Make a MATLAB program the calcul tes the n-th order divided difference of input zo .., . You will need the length command to identify the size of the input vector. 3. Make a MATLAB program that calculates the value of the n-th order interpolating polynomial (from Newton's equation) at a given point z. The input should be t and two vectors of interpolating points and the output should be the value of P(t). 4. Make a MATLAB program that graphs the interpolating polynomial The plot function works like this: t-sin(s plot(s,t You can type help plot to learn some of the other features, including how to plot in different colors