Question

The vertex of the graph of f(x) = |x – 3| + 6 is located at

Answer 1

Answer:

The answer is The vertex of the graph of f(x) = |x – 3| + 6 is located at (3,6)

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Step-by-step explanation:

Answer 2

Keywords:

Transformation of functions, vertical translations, horizontal translations

For this case we have to define function transformation:

Vertical translations:

Let $a> 0$, to graph $y = f (x) + a$, move the graph of $f (x)$ "a" upwards.

Horizontal translations:

Let $b> 0$, to graph $y = f (x-b)$, we must move the graph of $f (x)$"b" units to the right.

If we have as initial function $h (x) = | x |$

To obtain $g (x) = | x-3 |$ we move the graph of$h (x) = | x |$ three units on the right.

To obtain $f (x) = | x-3 | +6$ we move the graph of $g (x) = | x-3 |$six units up.

Thus, the vertex of$f (x) = | x - 3 | + 6$ is located at: $(x, y) = (3,6)$

Answer:

The vertex of the graph of $f (x) = | x - 3 | + 6$ is located at: $(x, y) = (3,6)$