Answer
a) Please see the graph.
b) $y=\operatorname{abs}\left(x-3\right)-4$ and $y=2\operatorname{abs}\left(x-3\right)-4$ open up, and the other two graphs open down.
c) If $a$ is positive, then the graph opens up. Otherwise, the graph opens down.
d) left side of $y=-\operatorname{abs}\left(x-3\right)-4$: $m=1$
right side of $y=-\operatorname{abs}\left(x-3\right)-4$: $m=-1$
left side of $y=\operatorname{abs}\left(x-3\right)-4$: $m = -1$
right side of $y=\operatorname{abs}\left(x-3\right)-4$: $m = 1$
left side of $y=-2\operatorname{abs}\left(x-3\right)-4$: $m=2$
right side of $y=-2\operatorname{abs}\left(x-3\right)-4$: $m=-2$
left side of $y=2\operatorname{abs}\left(x-3\right)-4$: $m=-2$
right side of $y=2\operatorname{abs}\left(x-3\right)-4$: $m=2$
e) The slope of the left side is -1* the slope of the right side. The slope of the right side is $a$, and the slope of the left side is $-a$.
Work Step by Step
a)
blue line: $y=-\operatorname{abs}\left(x-3\right)-4$
green line: $y=\operatorname{abs}\left(x-3\right)-4$
orange line: $y=-2\operatorname{abs}\left(x-3\right)-4$
purple line: $y=2\operatorname{abs}\left(x-3\right)-4$
b) The positive absolute value coefficient is what tells us which graphs open up.
c) The positive absolute value coefficient is what tells us which graphs open up.
d) The absolute value coefficient is the slope of the right side of the equation, and the slope of the left side of the graph is -1 * the absolute value coefficient.
e) As stated in part d, the absolute value coefficient is the slope of the right side of the equation, and the slope of the left side of the graph is -1 * the absolute value coefficient.
