Question

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

Answer 1

Find the x coordinate of the vertex, set x-2 to equal zero or x-2=0.
Since -2 is not the variable to solve for, move to right side of equation by adding 2 to both sides for x=2.
Replace the x variable with 2 in the expression to get y=|(2)-2|-7.
Simplify |(2)-2)|-7 to get -7 since 2-2=0.
Now becomes, y=0-7 then subtract 0-7=-7 to get y=-7.
The absolute value vertex is (2,-7)

Answer 2

The vertex of the absolute function is (2,-7).

Explanation:

Given : The absolute value function defined by
`f(x)=|x-2|-7` .

To find : What is the vertex of the absolute value function?

Solution :

In general, the graph of absolute function(V shaped) is defined by the equation,

`f(x)=a|x-h|+k`

where, (h,k) are the vertex of the equation slope m=a

Comparing the given equation with the general equation,

`f(x)=|x-2|+(-7)`

we get, h=2 and k=-7

Therefore, The vertex of the absolute function is (2,-7).

We can verify this by plotting the graph and see the vertex over there.

Refer the attached figure below.