# 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?

Vertex is $\left(0 , k\right)$
Consider $y = | x |$, the case where $k = 0$. This is two straight lines, $y = - x$ for $x < 0$ and $y = x$ for $x \ge 0$ - 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 $\left(x , y\right) = \left(0 , k\right)$. So we expect to see three Vs above each other: