If an absolute value function has a vertex at and opens upward with a vertical compression by a factor of , its equation is .
Answer & Analysis
Analysis
Question Analysis
This question evaluates the skill of writing an absolute value function with a given vertex, direction of opening, and vertical compression.
Key Concept Explanation
In the general form , the value of dictates both the direction of opening and the vertical stretch or compression.
Step-by-step Solution
1. Identify the vertex: .
2. Determine : The graph opens upward and is compressed by a factor of , so .
3. Substitute ,
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