y = polyval(p,x)
[y,delta] = polyval(p,x,S)
y = polyval(p,x,,mu)
[y,delta] = polyval(p,x,S,mu)
y = polyval(p,x) returns the value of a polynomial of degree n evaluated at x. The input argument p is a vector of length n+1 whose elements are the coefficients in descending powers of the polynomial to be evaluated.
y = p1xn + p2xn–1 + … + pnx + pn+1
x can be a matrix or a vector. In either case, polyval evaluates p at each element of x.
[y,delta] = polyval(p,x,S) uses the optional output structure S generated by polyfit to generate error estimates delta. delta is an estimate of the standard deviation of the error in predicting a future observation at x by p(x). If the coefficients in p are least squares estimates computed by polyfit, and the errors in the data input to polyfit are independent, normal, and have constant variance, then y±delta contains at least 50% of the predictions of future observations at x.
The polynomial is evaluated at x = 5, 7, and 9 with
p = [3 2 1]; polyval(p,[5 7 9])
which results in
ans = 86 162 262
For another example, see polyfit.