In the same coordinate plane, graph y= lxl + k for k= -2, 0, 2. What effect does k have on the graph of y= lxl +k ? what is the vertex of the graph y= lxl +k?

1 Answer
Jun 19, 2018

Vertex is (0,k)

Explanation:

Consider y=|x|, the case where k=0. This is two straight lines, y=-x for x<0 and y=x for x>=0 - it's a V shape, with the vertex at the origin. When we add k to it, the vertex is shifted up or down depending on the sign of k - the vertex being at (x,y)=(0,k). So we expect to see three Vs above each other:
graph{(y-|x|+2)(y-|x|)(y-|x|-2)=0 [-12.34, 12.97, -3.24, 9.42]}