What is the vertex of the graph of $g(x)=|x-8|+6$?

A. $(6,8)$
B. $(8,6)$
C. $(6,-8)$
D. $(-8,6)$

The function is in the form g ( x ) = ∣ x − 8∣ + 6 .
Identify the vertex form of an absolute value function: f ( x ) = ∣ x − h ∣ + k , where the vertex is ( h , k ) .
In this case, h = 8 and k = 6 .
The vertex of the graph is ( 8 , 6 ) ​ .

Explanation

Understanding the Function The given function is g ( x ) = ∣ x − 8∣ + 6 . We need to find the vertex of the graph of this absolute value function.

Identifying the Vertex Form The vertex of an absolute value function f ( x ) = ∣ x − h ∣ + k is at the point ( h , k ) . In our case, g ( x ) = ∣ x − 8∣ + 6 , so we can identify h = 8 and k = 6 .

Determining the Vertex Therefore, the vertex of the graph of g ( x ) = ∣ x − 8∣ + 6 is ( 8 , 6 ) .


Examples
Absolute value functions are used in various real-world applications, such as determining the distance from a target in engineering or physics. For example, if you're aiming for a specific temperature in a chemical reaction, the absolute value function can help you calculate the deviation from the target, regardless of whether the temperature is above or below the desired value. Similarly, in manufacturing, absolute value functions can be used to ensure that parts are within a specified tolerance range, measuring the difference between the actual size and the ideal size.

Answered by GinnyAnswer | 2025-07-06

The vertex of the graph of the function g ( x ) = ∣ x − 8∣ + 6 is located at the point ( 8 , 6 ) , resulting in the answer choice being option B. This point represents the minimum value of the function.
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Answered by Anonymous | 2025-08-04