Since the parabola opens downwards, the vertex represents the maximum point. The maximum function value is the y-coordinate of the vertex, which is 4. This maximum occurs at x = 2.

The domain, representing all possible x-values, is all real numbers (from negative infinity to positive infinity) because the graph extends infinitely horizontally. The range, representing all possible y-values, extends from negative infinity up to and including the maximum y-value of the vertex, which is 4. So, the range is (-∞, 4].

The parabola opens downward, indicating a high point which is the vertex. The vertex is at (2, 4). This point also lies on the axis of symmetry, a vertical line with the equation x = 2, where the parabola is symmetrical.

The function is increasing as x increases from negative infinity to the x-coordinate of the vertex (x=2). It is decreasing as x increases from the x-coordinate of the vertex (x=2) to positive infinity. The vertex itself is neither increasing nor decreasing.

The x-intercepts are where the graph crosses the x-axis, which are at (-2, 0) and (6, 0). The y-intercept is where the graph crosses the y-axis, located at (0, 3).