Question
Describe the translation of the function y=(x−1)2+3 (1 point) Responses translated down 3 units and right 1 unit translated down 3 units and right 1 unit translated down 3 units and left 1 unit translated down 3 units and left 1 unit translated up 3 units and left 1 unit translated up 3 units and left 1 unit translated up 3 units and right 1 unit
Answers
GPT-4o mini
To analyze the function \( y = (x - 1)^2 + 3 \), we can understand the transformations applied to the graph of the basic quadratic function \( y = x^2 \).
1. **The term \( (x - 1)^2 \)** indicates a horizontal translation. Specifically, the graph of \( y = x^2 \) is translated to the right by 1 unit (because of \( -1 \) in \( x - 1 \)).
2. **The \( +3 \)** indicates a vertical translation. The graph is shifted up by 3 units.
Therefore, the function \( y = (x - 1)^2 + 3 \) represents the original parabola \( y = x^2 \) translated right 1 unit and up 3 units.
Now considering the list of responses provided, none of them exactly describe the transformations that correspond to the function \( y = (x - 1)^2 + 3 \).
Here’s how each provided option compares to the analyzed function:
- **Translated down 3 units and right 1 unit** - does not match.
- **Translated down 3 units and left 1 unit** - does not match.
- **Translated up 3 units and left 1 unit** - does not match.
- **Translated up 3 units and right 1 unit** - matches, as this correctly describes the translation of this function.
The answer is **translated up 3 units and right 1 unit**.
1. **The term \( (x - 1)^2 \)** indicates a horizontal translation. Specifically, the graph of \( y = x^2 \) is translated to the right by 1 unit (because of \( -1 \) in \( x - 1 \)).
2. **The \( +3 \)** indicates a vertical translation. The graph is shifted up by 3 units.
Therefore, the function \( y = (x - 1)^2 + 3 \) represents the original parabola \( y = x^2 \) translated right 1 unit and up 3 units.
Now considering the list of responses provided, none of them exactly describe the transformations that correspond to the function \( y = (x - 1)^2 + 3 \).
Here’s how each provided option compares to the analyzed function:
- **Translated down 3 units and right 1 unit** - does not match.
- **Translated down 3 units and left 1 unit** - does not match.
- **Translated up 3 units and left 1 unit** - does not match.
- **Translated up 3 units and right 1 unit** - matches, as this correctly describes the translation of this function.
The answer is **translated up 3 units and right 1 unit**.