The axis of symmetry of a parabola is x = h, where h is the x-coordinate of the vertex.
From the picture, the vertex of the parabola is located at (3, 2), then the axis of symmetry is x = 3
Parabola in vertex form:
y = a(x -h)² + k
where (h, k) is the vertex. Replacing with (3, 2) as the vertex
y = a(x -3)² + 2
The point (1, -2) is on the parabola, then
-2 = a(1 -3)² + 2
-2 = a(-2)² + 2
-2 = a(4) + 2
-2 - 2 = a(4)
-4/4 = a
-1 = a
The equation is:
y = -(x -3)² + 2