Question
What is the vertex of the graph of \( g(x)=|x-8|+6 \) ? \( (6,8) \) \( (8,6) \) \( (6,-8) \) \( (-8,6) \)
Ask by Mccoy Norton. in the United States
Jan 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The vertex is at \( (8,6) \).
Solution
The function given is \( g(x) = |x - 8| + 6 \). This is in the form of \( g(x) = |x - h| + k \), where the vertex of the graph is at the point \( (h, k) \).
Comparing the two:
- \( h = 8 \)
- \( k = 6 \)
Therefore, the vertex of the graph is at \( (8, 6) \).
**Answer:** \( (8,6) \)
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Simplify this solution Beyond the Answer
The vertex of the graph of \( g(x) = |x-8| + 6 \) occurs at the point where the expression inside the absolute value equals zero. This happens when \( x = 8 \). Substituting \( x = 8 \) back into the function gives \( g(8) = |8 - 8| + 6 = 0 + 6 = 6 \). Therefore, the vertex is at the coordinates \( (8, 6) \). To help visualize this, remember that the graph of \( g(x) \) is a V-shape centered around the vertex. The "V" opens upwards and reaches its minimum value at the vertex. This means that every point on the graph to the left and right of the vertex increases in value, making the vertex the "lowest" point on the graph.
