To find the vertex of the function [tex]\( y = |x - 2| \)[/tex], we need to follow a few steps:
1. Understand the structure of the absolute value function:
The general form of an absolute value function is [tex]\( y = |x - h| \)[/tex], where [tex]\( h \)[/tex] is the value that shifts the graph horizontally.
2. Vertex of the general absolute value function:
For the function [tex]\( y = |x - h| \)[/tex], the vertex occurs at the point [tex]\( (h, 0) \)[/tex]. This is because when [tex]\( x = h \)[/tex], the expression inside the absolute value becomes zero, making [tex]\( y = 0 \)[/tex].
3. Identify the shift in the given function:
In the given function [tex]\( y = |x - 2| \)[/tex], we compare this with the general form [tex]\( y = |x - h| \)[/tex]. Here, [tex]\( h \)[/tex] is 2. This indicates that the graph is shifted 2 units to the right.
4. Determine the coordinates of the vertex:
Since [tex]\( h = 2 \)[/tex], the vertex occurs at [tex]\( (2, 0) \)[/tex].
Therefore, the vertex of the function [tex]\( y = |x - 2| \)[/tex] is at the point [tex]\( (2, 0) \)[/tex].
So, the correct answer is:
[tex]\[ (2, 0) \][/tex]
