Final answer:
The vertex is (3/2, 0) and the axis of symmetry is x = 3/2.
Step-by-step explanation:
The given equation is y = -x² + 3x².
To determine the vertex and axis of symmetry, we can rewrite the equation in the vertex form, which is y = a(x - h)² + k. In this form, the vertex is represented by the point (h, k) and the axis of symmetry is the vertical line x = h.
Comparing the given equation to the vertex form, we can see that a = -1, h = 3/2, and k = 0. Therefore, the vertex is (3/2, 0) and the axis of symmetry is x = 3/2.