For a positive number k, the function y=-|x|-k translates the entire graph of y=-|x| downwards by k units.
y=-|x|-15
Practice makes perfect
For a positive number k, the function y=-|x|-k translates the entire graph of y=-|x| downwards k units. Let's start by drawing the graph of y=-|x|, which is the reflection of the graph of the absolute valueparent function along the x-axis.
Now let's translate all points on this graph 15 units down. To do so, we just need to decrease each y-coordinate by 15. As an example, we will translate three points on the line y=-|x| downwards 15 units.
Translating each and every point 15 units down means shifting the entire graph of y=-|x| down by 15 units.
Therefore, the resulting equation will be y=-|x|-15.
