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

Mar 30, 2018

#### Explanation:

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 $f \left(x\right) = | x |$ is compressed horizontally to produce the graph of $y = | b x |$.

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