Answer:
well, the cheap answer is
f(x) = -3| x - 1 | is really just f(x) = -3| x - 1 | + 0.
now, what value of "x" makes the absolute value expression to 0?
well, let's just set it to 0 and check,
x - 1 = 0
x = 1
so if "x" ever becomes 1, the | x - 1| will turn to 0, therefore, the vertex is at
f(x) = -3| (1) - 1 | + 0 --------------> ( 1, 0 )
