Answer:
y = (x -3)² -2
Explanation:
The vertex form of the equation of a parabola is ...
y = a(x -h)² + k
for vertex (h, k) and vertical scale factor "a".
Your graph shows the vertex to be at (x, y) = (3, -2). Note that one unit either side of the vertex, the graph goes up one unit. The number of vertical units difference from the vertex is the value of "a", so it is 1 for this parabola.
That means the equation is ...
y = 1·(x -3)² -2
or, more simply, ...
y = (x -3)² -2 . . . . . . . matches the 3rd choice
_____
Please note that if "a" is negative, the parabola will open downward. This one opens upward, so you can immediately reject the first two answer choices.