The x coordinates are all spaced by 1 unit. The gradients between each successive point are:
2, 1, 1, 2 (just the difference between successive y coordinates)
The second gradients are -1, 0, 1.
Let's compare with a simple quadratic: y=ax2+bx+c.
Let's use the same x coordinates from -2 to 2 and calculate the y coordinates:
(-2,4a-2b+c), (-1,a-b+c), (0,c), (1,a+b+c), (4a+2b+c).
First gradients are: -3a+b, -a+b, a+b, 3a+b.
Second gradients are: 2a, 2a, 2a (a constant).
So the given points are not from a quadratic function.