Page "Rational normal curve" Paragraph 19

is a rational normal curve.

That this is a rational normal curve may be understood by noting that the monomials are just one possible basis for the space of degree-n homogeneous polynomials.

In fact, any basis will do.

This is just an application of the statement that any two projective varieties are projectively equivalent if they are congruent modulo the projective linear group ( with K the field over which the projective space is defined ).