Question

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

Answer 1

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

Answer 2

The vertex is at

`(2,-7)`

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)`