How do I find the rule?
Is one of those points the vertex? Aren't those 3 points in a straight line; like I can't get the equations of two linear functions and find the vertex by finding their point of intersection if they're straight. Sorry if I've missed something, I'm a bit tired from studying all day.
having to find an absolute value function, I would sketch a graph with points at (0,86) (3,68) (6,50) (9,68) (12,86).
connecting the points using lines, one can see the large "V" indicating a transformed version of y = |x|.
slope is 6 ...
y = 6|x|
horizontal shift to the right 6 units ...
y = 6|x-6|
vertical shift up 50 units ...
y = 6|x-6| + 50
but, again, the problem statement should have been more clear in relating what was required as a solution.