We know that the vertical asymptotes are x=1 and x=-1. We also know that we get vertical asymptotes for values of x for which there are no values of y; that is to say at these values of x the denominator of the fraction must be zero.

So we have (1)^2 + (1)b + c = 0

and (-1)^2 + (-1)b + c = 0

Two equations and two unknowns, so solving them simultaneously, we get b = 0 and c = -1.

So how do we find k? We know that (0, -3) is a point on this graph, so we can substitute in, x=0, y=-3, and the values of b and c we just found into the original equation of the graph. Hence we get k=3.

[Alternatively, you could think of the last step as a scaling of the graph parallel to the y axis by factor 3, so k=3]