Question
Create an equation that models the transformation of y=2x2 to the function in the graph. (1 point) Responses y=2x2−4 y equals 2 x squared minus 4 y=2x2+4 y equals 2 x squared plus 4 y=2(x+4)2 y equals 2 left parenthesis x plus 4 right parenthesis sqaured y=2(x−4)2
Answers
GPT-4o mini
To determine which equation models the transformation of \( y = 2x^2 \) to the function in the graph, we need to consider any vertical shifts, horizontal shifts, or changes in the coefficient.
1. **Identifying the original function**: The original function is \( y=2x^2 \).
2. **Vertical shifts**: If there is a +4 at the end, it means the graph shifts upward by 4 units. If there is a -4 at the end, it shifts downward by 4 units.
3. **Horizontal shifts**: If there is a (x + k) term inside the function, the graph shifts horizontally. For example, (x + 4) shifts left by 4 units, while (x - 4) shifts right by 4 units.
Now let's analyze the options given:
- **Option 1**: \( y = 2x^2 - 4 \) (downward shift by 4 units)
- **Option 2**: \( y = 2x^2 + 4 \) (upward shift by 4 units)
- **Option 3**: \( y = 2(x + 4)^2 \) (leftward shift by 4 units)
- **Option 4**: \( y = 2(x - 4)^2 \) (rightward shift by 4 units)
Without the specific graph to analyze, I cannot definitively state which equation models the transformation without knowing the specific shifts of the graph.
However, you should compare the original function to the transformations indicated by the options above. If you provide a description of the changes on the graph, I can help determine which equation fits best!
1. **Identifying the original function**: The original function is \( y=2x^2 \).
2. **Vertical shifts**: If there is a +4 at the end, it means the graph shifts upward by 4 units. If there is a -4 at the end, it shifts downward by 4 units.
3. **Horizontal shifts**: If there is a (x + k) term inside the function, the graph shifts horizontally. For example, (x + 4) shifts left by 4 units, while (x - 4) shifts right by 4 units.
Now let's analyze the options given:
- **Option 1**: \( y = 2x^2 - 4 \) (downward shift by 4 units)
- **Option 2**: \( y = 2x^2 + 4 \) (upward shift by 4 units)
- **Option 3**: \( y = 2(x + 4)^2 \) (leftward shift by 4 units)
- **Option 4**: \( y = 2(x - 4)^2 \) (rightward shift by 4 units)
Without the specific graph to analyze, I cannot definitively state which equation models the transformation without knowing the specific shifts of the graph.
However, you should compare the original function to the transformations indicated by the options above. If you provide a description of the changes on the graph, I can help determine which equation fits best!