What is the equation of the axis of symmetry for the parabola y equals start fraction one over three end fraction left parenthesis x plus one right parenthesis squared minus three?

The correct axis of symmetry is x = -1.

Explanation:

Our equation is
.

This is in vertex form, which is 
y = a(x-h)² + k, where (h, k) is the vertex.

In our equation, h corresponds with -1 and k corresponds with -3, making the vertex (-1, -3).

The axis of symmetry is the x-coordinate of the vertex; this makes the axis of symmetry for this equation x = -1.