For the graph of the function below, identify the axis of symmetry, vertex and formula for the function

Well the first obvious thing is that the axis of symmetry is 0.5, so we can automatically cross out (C).

All the answers have the correct vertex, so lets find the formula for the function.

Fortunately, from my point of view, I can see two points that have their coordinates as integers, (-1, -3) and (2, 3), we can plug these into the already given "formulas" in the options (A), (B), and (D).

Out of the three choices, the formula in option (D) satisfies both coordinates, thus option (D) is correct.