How do you graph #y=-2abs(5x+8)+4#?

Consider the General Form of the Absolute Value Function:

#color(red)(y=f(x) = a|bx-h|+k#

#color(red)(a# - responsible for Compressing/Stretching the graph.

#color(red)(b# - When #color(red)(|b| > 1#, the graph of #f(x) = |x|# is compressed horizontally to produce the graph of #y=|bx|#.

It is interesting to note that the the sign of b does not affect the graph since the absolute value is considered.

#color(red)(h# - responsible for Shifting the graph left/right.

#color(red)(k# - responsible for Shifting the graph up/down.

The Parent Function is of the form #color(blue)(y=f(x)=|x|#

The absolute value function #color(blue)(y=-2abs(5x+8)+4# involve transformations.

Complete table of values for the graph:

Analyze the behavior of the graph (in stages) of the given absolute value function:

(Images of graphs are in sequence to enable visual comprehension)

Graph 1 Graphs of #color(blue)(y=|x| and y = |5x|#

Graph 2 Graphs of #color(blue)(y=|x| and y = |5x + 8|#

Graph 3 Graphs of #color(blue)(y=|x| and y = -2 |5x + 8|#

A negative value for #a# results in a reflection across the x-axis.

Graph 4 Graphs of #color(blue)(y=|x| and y = -2 |5x + 8| + 4#