Respuesta :

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 )

Using concepts of the absolute value function, it is found that the vertex is at (1,0).

The general absolute value function can be modeled as:

[tex]f(x) = a|x - b| + c[/tex]

The vertex is at (b,c).

In this problem, the function is:

[tex]f(x) = -3|x - 1|[/tex]

Thus, [tex]a = -3, b = 1, c = 0[/tex], which means that the vertex is at (1,0), which is confirmed by the sketch of the graph at the end of this answer.

A similar problem is given at https://brainly.com/question/24559165

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