We see that the differences are -9, -3, +3, and +9. Thus, we see that the function is symmetric about x=2 (I'm assuming the five values correspond to x=0, 1, 2, 3, 4) and increases at a rate similar to (x-2) squared. With that in mind, we classify this function as a parabola, as the standard form of a parabola (y=a(x-h)^2 + k) shows similar growth to this function.
I disagree. If each side of the equation is divided by 5, the result is x2 = 4. By the square root property of equality, x = -2 or x = 2. So x could be -2 instead of 2.