Final answer:
To determine a sixth-degree polynomial function, look for an expression with the highest variable power of 6, such as anx6, without any higher powers of x. Quadratic equations are second-degree polynomials and differ from sixth-degree polynomials.
Step-by-step explanation:
To identify a sixth-degree polynomial function, you need to look for an algebraic expression where the highest power of the variable (usually represented as x) is 6. This means that one of the terms will be in the form of anx6 where an is a non-zero coefficient. Such a function can have up to six roots (solutions), can change direction up to five times as it crosses the x-axis, and will generally have a complex graph with multiple turning points.
As a reminder, the solution of quadratic equations deals with second-degree polynomials (functions where the highest power of x is 2). In contrast, a sixth-degree polynomial is far more complex.
To determine which expressions are sixth-degree polynomial functions, you would look for terms like x6, and you would not see any higher powers of x. Expressions that contain x to the power of 7 or higher are not sixth-degree polynomials. The coefficients of x can be positive, negative, or fractional, and the polynomial can have constant terms as well as other lower-degree terms (x5, x4, etc.).