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What is the vertex point of y = |x - 2| + 3? Enter your answer as an ordered pair, e.g. (1,2).

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Answer:

Vertex: (2, 3).

Step-by-step explanation:

Definition of terms:

The general form of an absolute function is given by: y = a|x - h| + k, where:

| a | ⇒ Determines the vertical stretch or compression factor of the function.

(h, k) ⇒ Coordinates of the vertex, which is either the minimum or maximum point on the graph.

x = h ⇒ Axis of symmetry, which is the imaginary vertical line that splits the graph of the function into two symmetrical parts.

Explanation"

Given the absolute value function, y = |x - 2| + 3:

Based on the general form of absolute value functions described in the previous section of this post, y = a|x - h| + k:

We can assume that the value of "a" in the given absolute value function is 1, because if we distribute 1 into the terms inside the bars, "|    |," the constant value of a = 1 will not change the value of those terms.  

  • However, there are other instances where there is a given value for "a," which could either "stretch" or "compress" the graph of the absolute value function.  If the value of | a | > 1, then it represents the vertical stretch (the graph appears narrower than the parent graph of the absolute value function). In contrast, if the the value of "a" is 0 < | a | < 1, then it represents a vertical compression (the graph appears wider than the parent graph of the absolute value function).

In terms of the vertex, it occurs at point, (2, 3), where h = 2, and k = 3.  

Therefore, the vertex of the given absolute value function is (2, 3).

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