Question

How do you graph D? PLz explain. HELPPPPPPPPPPPPPPP

Answer 1

See the attached image for the graph. Specifically figure 2 is the graph you want. You can leave the red points on the graph or decide to erase them (leave behind the blue line though). 

To generate each of the red points, you'll plug in various x values to get corresponding y values.

For instance, plug in x = 0 and we get...
y = -|x-6| - 6
y = -|0-6| - 6
y = -|-6| - 6
y = -6 - 6
y = -12
So when x = 0, the y value is -12. The x and y value pair up to get (x,y) = (0,-12)

Another example: plug in x = 2
y = -|x-6| - 6
y = -|2-6| - 6
y = -|-4| - 6
y = -4 - 6
y = -10
So the point (2,-10) is on the graph

The idea is to generate as many points as possible so we get an idea of what this thing looks like. 

Generate enough points, and you'll get what you see in Figure 1 (see attached image)

Then draw a line through all of the points. The more points you use, the more accurate the drawing. Doing that will generate the blue function curve you see in Figure 2 (also attached)

Answer 2

The general form of an absolute value function can be expressed as follows:

y = a|x - h| + k   where (h,k) is the vertex of you graph, and 'a' will determine the slope of the two halves of the graph as well as whether the graph opens up or down.

Given:   y = -|x - 6| - 6  this graph will have a vertex at (6, -6), the graph will open down with a slope of 1 from (-∞, 6] and a slope of -1 from [6, ∞)