How do you graph #y = -abs(x+6)#?

1 Answer
George C.
Jul 5, 2015

This is an upside-down V shape with arms having slope #+-1# and vertex at #(-6, 0)#

Explanation:

#abs(x+6) = x+6# when #x+6 >= 0#, that is when #x >= -6#
So #y = -abs(x+6) = -x-6# has slope #-1# when #x >= -6#

#abs(x+6) = -(x+6)# when #x+6 < 0#, that is when #x < -6#
So #y = -abs(x+6) = x+6# has slope #1# when #x < -6#

The vertex is at the point where #(x+6) = 0#, giving #x = -6# and #y = 0#. So the vertex is at #(-6, 0)#

The intersection with the #y# axis will be where #x=0#. Substituting #x=0# into the equation, we get #y = -abs(6) = -6#. So the intersection is at #(0, -6)#

graph{-abs(x+6) [-13.63, 6.37, -6.96, 3.04]}

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