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
MoominDave
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]}

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