Finding the Vertex of an Absolute Value Function

Given :
g(x) = |x+1| + 3

Look at the absolute value section |x + 1|

What would x have to be to get the value of 0 inside the absolute value? Zero is the lowest possible value that could come out of the absolute value function. Answer x = -1 (this will give us the smallest value for y that could come out of the absolute value - zero).
So x = -1 is the x value of the vertex (where y has its lowest value)

So if the value of x is -1 then y = |-1 + 1| + 3 or 3.

So the vertex is (-1,3)
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Let's look at

g(x) = -|1/2x - 1| + 5

What would the value of x have to be to have 0 inside the absolute value? Answer : x = 2
So the x vertex is 2

So y, at the vertex = -|1/2 (2) - 1| + 5 or 5
So the value for the y vertex is 5

Vertex is (2,5)

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g(x) = |1/3x + 1| - 7

1/3x + 1 = 0
So x = -3 so value of x vertex is -3

So y = |1/3(-3)| - 7 so y's value at the vertex is -7.

So vertex is (-3,-7)

Fit it in to see if it works :
-7 = |1/3(-3) - 1| - 7
-7 = |0| - 7
-7 = -7
So we have found the vertex