Final answer:
The function y = -|4x+5| -2 transforms the parent function y = |x| with a reflection, horizontal compression, and translations. The vertex is at (-5/4, -2), and the axis of symmetry is x = -5/4.
Step-by-step explanation:
When comparing the function y = -|4x+5| -2 to the parent function y = |x|, several transformations can be observed. The parent function has a vertex at the origin (0,0), and its axis of symmetry is the y-axis. For the given function, the negative sign in front of the absolute value indicates a reflection over the x-axis. The factor of 4 within the absolute value means the graph is horizontally compressed by a factor of 1/4. The addition of 5 inside the absolute value translates the graph left by 5/4 units, while the subtraction of 2 outside of it moves the graph down by 2 units. The vertex of this transformed function is at (-5/4, -2), and the axis of symmetry is the vertical line x = -5/4.