Question
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Without graphing, identify the vertex, axis of symmetry, and transformations from the parent function \( f(x)=|x| \) \[ y=|x-4|+3 \] The vertex is \( (4,3) \). (Type an ordered pair.) The axis of symmetry is \( x=\square \)

Ask by Bryant Hills. in the United States
Jan 31,2025

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Answer

- **Vertex:** \( (4, 3) \) - **Axis of Symmetry:** \( x = 4 \) - **Transformations:** - Shifted 4 units to the right - Shifted 3 units up

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The Deep Dive

The axis of symmetry is \( x=4 \). This transformation takes the parent function \( f(x)=|x| \) and shifts it 4 units to the right and 3 units up. Essentially, every point on the V-shaped graph moves in tandem to create the new vertex at \( (4,3) \). Think of it as moving the whole mountain to a new spot in the valley!

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