A vertex is a corner or a point where edges meet. For a cone, it is the sharp point at the top.
Full Answer
A vertex is a point where two or more lines or edges meet. In the context of a cone, the vertex is the apex, which is the sharp point at the top.
A cone has one circular base and a curved surface that tapers to the vertex. The circular base does not have any corners, so the only vertex is the apex.
Therefore, a cone has 1 vertex.
Common mistakes
✗ Confusing vertices with faces or edges.
✗ Thinking the circular base has vertices (it doesn't).
✗ Answering 0.