This is the equation of a horizontal parabola whose vertex is on the left side and opens to the right.
To find the vertex, complete the square:
x = y2 - y + 2
x - 2 = y2 - y
x - 2 + ¼ = y2 - y + ¼ (complete the square)
x - 7/4 = (y - ½)2
The vertex is (7/4, 1/2)