Answer:
Vertex: (2, 3).
Step-by-step explanation:
<h2><u>Definition of terms:</u></h2>
The general form of an absolute function is given by: y = a|x - h| + k, where:
| <em>a </em>| ⇒ Determines the vertical <em>stretch</em> or <em>compression</em> factor of the function.
(h, k) ⇒ Coordinates of the <u>vertex</u>, which is either the minimum or maximum point on the graph.
x = h ⇒ <u>Axis of symmetry</u>, which is the imaginary vertical line that splits the graph of the function into two symmetrical parts.
<h2><u>Explanation"</u></h2>
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 "<em>a</em>" 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 | <em>a</em> | > 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 < | <em>a</em> | < 1, then it represents a <u>vertical compression</u> (the graph appears <u>wider</u> than the <em>parent graph</em> of the absolute value function).
In terms of the <u>vertex,</u> it occurs at point, (2, 3), where <em>h</em> = 2, and <em>k</em> = 3.
Therefore, the vertex of the given absolute value function is (2, 3).
