Question

What is the vertex of the absolute value function defined by ƒ(x) = |x - 2| - 7?

Answer 1

Answer:

The vertex is at

$(2,-7)$

Step-by-step explanation:

We can get the vertx by graphing or by analysing the function.

Let's analyse.

The parent function of the given one is

$g(x)=|x|$

And the given one is $f(x)=|x-2|-7$

Specifically, the given function is a transformed function moved 2 units rightwards and 7 downwards.

We know that the parent function has vertex at $(0,0)$, but with these decribed transformation, the function has vertex at $(2,-7)$.

You can see this in the image attached, which shows the given function and its vertex.

Therefore, the vertex is at $(2,-7)$

Answer 2

X - 2 = 7 , x - 2 = - 7
x = 9 , x = - 5