1. First draw the graph f(x)=|x|. On the interval x>0 or =0, the graph is a ray drawn from the Origin (0, 0) and goes straight upwards at slope of 1:1. Slope is the ratio of units change in y to a unit change in x. So, the value y increases 1 unit as x increases 1 unit.
2. On the interval x<0, the graph f(x)=|x| is the mirror image of right-hand ray reflected about the y-axis. The slope of the left-hand ray is (-1):1. So, the value of y decreases 1 unit as x increases 1 unit.
Now, we have the graph f(x)=|x|. The 2 rays open up/point down forming a letter-V vertex (holds water) at the bottom. The vertex corresponds to the Origin (0, 0). The y-axis is the line of symmetry.
3. f(x)=|x+8| is f(x)=|x| moved horizontally 8 units to the left. You need not draw a new graph, but just draw a vertical line 8 units right from the original y-axis. That is the new y-axis. The right-hand ray intersects the new y-axis at y=8. Change the old marks on the x-axis to the new ones.
Now we have the graph asked f(x)=|x+8|. the vertical line x=-8 is the line of symmetry, and the coordinates of the vertex are x=-8 and y=0, or (-8, 0).
The answer: The graph opens up forming a letter-V vertex at point (-8, 0)