Examining the y-values shows that all of the given y-values are perfect squares. Further, the graph dips at first, reaches a minimum (-1,0) and then increases as does the second power of x.
This is sufficient info on which to base the conclusion that the vertex of this parabolic function is at (-1,0), and that the axis of symmetry (which goes thru the vertex) is x = -1.
The most basic form of the equation of a parabola is y = x^2. The graph is that of a parabola and opens up. The vertex is (0,0) and the axis of symmetry is x=0.
In this particular case, the vertex has been translated 1 unit to the left. The corresponding equation of this "new" parabola is y = (x+1)^2. Note that (2,9) (one of the points given in the table) satisfies this equation:
9 = (2+1)^2.
The desired equation is y = (x+1)^2.