Question 212735
To graph {{{y=-2*abs(x+1)-4}}}, simply follow the given steps below:



Step 1) Graph {{{y=abs(x)}}}


{{{ graph( 500, 500, -10, 10, -10, 10, abs(x)) }}} Graph of {{{y=abs(x)}}}


Note: the graph of {{{abs(x)}}} is simply comprised of the lines {{{y=x}}} and {{{y=-x}}} (just don't graph the portion that lies below the x-axis).



Step 2) Shift {{{y=abs(x)}}} 1 unit to the left to get {{{y=abs(x+1)}}}


{{{ graph( 500, 500, -10, 10, -10, 10, abs(x),abs(x+1)) }}} Graph of {{{y=abs(x)}}} (red) and {{{y=abs(x+1)}}} (green)



Step 3) Vertically stretch {{{y=abs(x+1)}}} by a factor of 2 to get {{{y=2abs(x+1)}}} 



{{{ graph( 500, 500, -10, 10, -10, 10, abs(x+1),2*abs(x+1)) }}} Graph of {{{y=abs(x+1)}}} (red) and {{{y=2*abs(x+1)}}} (green)



Step 4) Reflect {{{y=2abs(x+1)}}} over the x axis to get {{{y=-2*abs(x+1)}}}



{{{ graph( 500, 500, -10, 10, -10, 10, 2*abs(x+1),-2*abs(x+1)) }}} Graph of {{{y=2*abs(x+1)}}} (red) and {{{y=-2*abs(x+1)}}} (green)



Step 5) Shift the entire graph of {{{y=-2*abs(x+1)}}} down 4 units to get {{{y=-2*abs(x+1)-4}}}



{{{ graph( 500, 500, -10, 10, -10, 10, -2*abs(x+1),-2*abs(x+1)-4) }}} Graph of {{{y=-2*abs(x+1)}}} (red) and {{{y=-2*abs(x+1)-4}}} (green)





So the graph of {{{y=-2*abs(x+1)-4}}} is 


{{{ graph( 500, 500, -10, 10, -10, 10, -2*abs(x+1)-4) }}} Graph of  {{{y=-2*abs(x+1)-4}}}