Question

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?

Answer 1

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]}