Final answer:
The given function, f(x) = 2(x - 3)^2 + 1, is a quadratic function.
Step-by-step explanation:
The given function, f(x) = 2(x - 3)^2 + 1, is a quadratic function.
A quadratic function is a polynomial function of degree 2, where the highest power of the variable is 2.
In this function, the variable is x and it appears as a squared term (x - 3)^2, which makes it a quadratic function.
Quadratic functions have a U-shaped graph and represent relationships where one variable depends on the square of another variable.