1. **State the problem:** We need to graph the function $$y=|x+5|-2$$ and find key points to plot. 2. **Recall the absolute value function:** The absolute value function $$|x|$$ outputs the distance of $$x$$ from zero, always non-negative. 3. **Transformations:** The function $$y=|x+5|-2$$ shifts the basic absolute value graph: - Horizontally left by 5 units (due to $$x+5$$ inside the absolute value). - Vertically down by 2 units (due to $$-2$$ outside). 4. **Find the vertex:** The vertex of $$y=|x+5|-2$$ is at $$x=-5$$ because $$|x+5|$$ is zero there. Calculate $$y$$ at $$x=-5$$: $$y=|(-5)+5|-2=|0|-2=0-2=-2$$ So vertex is $$(-5,-2)$$. 5. **Find points on either side of vertex:** - At $$x=-6$$: $$y=|-6+5|-2=|-1|-2=1-2=-1$$ - At $$x=-4$$: $$y=|-4+5|-2=|1|-2=1-2=-1$$ - At $$x=-7$$: $$y=|-7+5|-2=|-2|-2=2-2=0$$ - At $$x=-3$$: $$y=|-3+5|-2=|2|-2=2-2=0$$ 6. **Summary of points:** $$(-7,0), (-6,-1), (-5,-2), (-4,-1), (-3,0)$$ 7. **Graph features:** The graph is a "V" shape with vertex at $$(-5,-2)$$, opening upwards.