You would best do this by completing the square on the quadratic and subbing in the vertex they give you, like this:
Since the y coordinate of the vertex is 1/2 and we need to solve for c, set the
equal to 1/2 and solve for c, which is the whole point of what we are doing, right?
and 
and c = 4. So that's our answer!
Since the y coordinate of the vertex is 1/2 and we need to solve for c, set the