The axis of symmetry for f(x) occurs at x = -b/2a. In this case, x = -2.

Because a quadratic function graphs as a parabola, it is never "one-to-one" and therefore never invertible unless we restrict the domain. If we do so, the domain can be restricted to one side of the axis or the other. Since the original function is a squaring function, the inverse will be a square root. We will choose the positive square root as the inverse of the right-hand side of the parabola, and the negative square root as the inverse for the left. Finally, putting the function in vertex form (by completing the square) makes it possible to find the inverse algebraically:

f(x) = (x + 2)^{2} - 10

x + 10 = (y + 2)^{2}

y = - √(x + 10) - 2 for the inverse of the left side and y = √(x + 10) - 2 for the right