Exercise 28 Page 349

For a positive number $k,$ the function $y=\text{-}|x|-k$ translates the entire graph of $y=\text{-}|x|$ downwards $k$ units. Let's start by drawing the graph of $y=\text{-}|x|,$ which is the reflection of the graph of the absolute value parent function along the $x\text{-}$axis.

Now let's translate all points on this graph $15$ units down. To do so, we just need to decrease each $y\text{-}$coordinate by $15.$ As an example, we will translate three points on the line $y=\text{-}|x|$ downwards $15$ units.

Translating each and every point $15$ units down means shifting the entire graph of $y=\text{-}|x|$ down by $15$ units.

Therefore, the resulting equation will be $y=\text{-}|x|-15.$