This question has to do with self-reducibility.

Show how the optimization version of vertex cover problem is polynomial time-reducible to its decision version.

The optimization version, known as min vertex cover problem, is this --

given a graph G, find the minimum set of vertices that cover all the edges in G.

The decision version is this --

given a graph G and a constant k, is there a vertex cover of at most k vertices?

Here, we say a vertex covers an edge if and only if the vertex is an end-node of the edge.