Final answer:
The vertex of the quadratic equation y=2(x+4)²+1 is (-4, 1) and the axis of symmetry is x=-4.
Step-by-step explanation:
To find the vertex and axis of symmetry of the quadratic equation y=2(x+4)²+1, we take the general form of a vertex equation, which is y=a(x-h)²+k, where (h, k) is the vertex and x=h is the axis of symmetry. In this case, a=2, h=-4, and k=1. Therefore, the vertex of the given equation is (-4, 1) and the axis of symmetry is x=-4.