Without graphing, identity the vertex, axis of symmetry, and transformations from the parent furcion f(t) \( =x \). \[ y=|x-2|+4 \] The ventex is (Type an ordered par)

To identify the vertex, axis of symmetry, and transformations from the parent function \( f(t) = |x| \) for the function \( y = |x - 2| + 4 \), we can follow these steps: 1. **Identify the transformations**: - The expression \( |x - 2| \) indicates a horizontal shift. The graph of \( |x| \) is shifted to the right by 2 units. - The \( +4 \) indicates a vertical shift. The graph is shifted upward by 4 units. 2. **Determine the vertex**: - The vertex of the parent function \( f(t) = |x| \) is at the origin (0, 0). - After applying the transformations: - Shift right by 2: The x-coordinate of the vertex becomes \( 2 \). - Shift up by 4: The y-coordinate of the vertex becomes \( 4 \). - Therefore, the vertex is at the point \( (2, 4) \). 3. **Identify the axis of symmetry**: - The axis of symmetry for the absolute value function is a vertical line that passes through the vertex. Since the vertex is at \( (2, 4) \), the axis of symmetry is the line \( x = 2 \). Now, summarizing the results: - The vertex is \( (2, 4) \). - The axis of symmetry is \( x = 2 \). Thus, the vertex is: \[ (2, 4) \]