Question 4 (1 print) Without graphing, identify the vertex, axis of symmetry, and transfiormations from the parent function fix \( =x x \) - \( y=|x-4|+6 \) The vertex is The axis of symmetry is \( x= \) What are the transformations from the parent function?

To analyze the function \( y = |x - 4| + 6 \), we can identify the vertex, axis of symmetry, and transformations from the parent function \( y = |x| \). 1. **Vertex**: The vertex of the function \( y = |x - 4| + 6 \) can be found from the expression inside the absolute value and the constant added outside. The vertex occurs at the point where the expression inside the absolute value equals zero. Setting \( x - 4 = 0 \) gives \( x = 4 \). The corresponding \( y \)-value is \( y = |4 - 4| + 6 = 0 + 6 = 6 \). Therefore, the vertex is \( (4, 6) \). 2. **Axis of Symmetry**: The axis of symmetry for an absolute value function in the form \( y = |x - h| + k \) is the vertical line that passes through the vertex. Since the vertex is at \( (4, 6) \), the axis of symmetry is \( x = 4 \). 3. **Transformations from the Parent Function**: The parent function is \( y = |x| \). The transformations applied to obtain \( y = |x - 4| + 6 \) are: - **Horizontal Shift**: The term \( x - 4 \) indicates a horizontal shift to the right by 4 units. - **Vertical Shift**: The \( +6 \) indicates a vertical shift upward by 6 units. In summary: - The vertex is \( (4, 6) \). - The axis of symmetry is \( x = 4 \). - The transformations from the parent function are a horizontal shift to the right by 4 units and a vertical shift upward by 6 units.