What is the maximum number of terms a fourth-degree polynomial function in standard form can have?

A polynomial of four terms is sometimes called a quadrinomial, but there's really no need for such words.
Likewise, what is a 4th degree polynomial? Fourth degree polynomials are also known as quartic polynomials. Quartics have these characteristics: Zero to four roots. One, two or three extrema. Zero, one or two inflection points.
The degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.
Zero Polynomial. The constant polynomial. whose coefficients are all equal to 0. The corresponding polynomial function is the constant function with value 0, also called the zero map. The zero polynomial is the additive identity of the additive group of polynomials.

The vertex of the quadratic function is (1.5, -.75)