To find the new vertex of the translated function starting from the parent function's vertex at (0, 0), we need to follow these steps:
1. Understand the translation parameters:
- We are required to move the vertex 2 units to the right.
- Also, we are required to move the vertex 4 units down.
2. Translation in the x-direction:
- Moving 2 units to the right means increasing the x-coordinate by 2.
- Initial x-coordinate: 0
- New x-coordinate: [tex]\(0 + 2 = 2\)[/tex]
3. Translation in the y-direction:
- Moving 4 units down means decreasing the y-coordinate by 4.
- Initial y-coordinate: 0
- New y-coordinate: [tex]\(0 - 4 = -4\)[/tex]
4. Combine the new coordinates:
- The new vertex is therefore (2, -4).
So, after translating the vertex 2 units to the right and 4 units down, the new vertex of the function will be at (2, -4).
