Final answer:
The vertex represents a maximum point.
Step-by-step explanation:
The vertex of a quadratic function represents either a maximum or a minimum point. To determine whether the vertex of the function f(x) = -x² - 4x + 2 represents a maximum or a minimum, we can look at the coefficient of the x² term.
Since the coefficient is negative (-1), this means that the parabola opens downward and the vertex represents a maximum point.