Vertex form

The vertex is (h, k) = (4, 1).

The axis of symmetry is x = h = 3.

a = 2, h = -4, k = -1.

The value of 'a' indicates the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

The equation has a maximum value.

A parabola is described as 'wider' when the absolute value of 'a' in the vertex form is less than 1 (|a| < 1).

If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

The vertex represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

You can convert by completing the square.