Question
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
Upstudy AI Solution
Tutor-Verified Answer
Answer
- **Vertex:** \( (4, 3) \)
- **Axis of Symmetry:** \( x = 4 \)
- **Transformations:**
- Shifted 4 units to the right
- Shifted 3 units up
Solution
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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!