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Vertex: (4, 0)

Axis of symmetry: x = 4

Step-by-step explanation:

This quadratic is in vertex form.  Vertex form is

y = a(x - h)² + k     where the point (h, k) is the vertex.  

For this equation we have

y = -(1/8)(x - 4)² + 0,   so our vertex is at the point (4, 0)  

*It's positive 4 because the equation is (x - h), so we're subtracting positive 4

The axis of symmetry is the equation of the vertical line that goes through the x coordinate of the vertex (quadratics are symmetric from the vertex)

So the axis of symmetry is x = 4