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Find the vertex of [tex]\( y = |x - 2| \)[/tex].

A. [tex]\((2, 2)\)[/tex]
B. [tex]\((0, 0)\)[/tex]
C. [tex]\((2, 0)\)[/tex]
D. [tex]\((0, 2)\)[/tex]

Sagot :

GinnyAnsweridn
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]
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