Question
Create an equation that models the transformation of y= 2x^2 to the function in the graph.
A: y=2(x +4)^2
B: y=2x^2 + 4
C:y= 2(x-4)^2
A: y=2(x +4)^2
B: y=2x^2 + 4
C:y= 2(x-4)^2
Answers
GPT-4o mini
To determine which equation models the transformation of \( y = 2x^2 \) to a new function given in graph form, we need to analyze the transformations represented by each option.
1. **Option A: \( y = 2(x + 4)^2 \)**
- This represents a horizontal translation of the graph of \( y = 2x^2 \) to the left by 4 units.
- The vertex of the parabola moves from \( (0,0) \) to \( (-4, 0) \).
2. **Option B: \( y = 2x^2 + 4 \)**
- This represents a vertical translation of the graph of \( y = 2x^2 \) upwards by 4 units.
- The vertex moves from \( (0,0) \) to \( (0, 4) \).
3. **Option C: \( y = 2(x-4)^2 \)**
- This represents a horizontal translation of the graph of \( y = 2x^2 \) to the right by 4 units.
- The vertex moves from \( (0,0) \) to \( (4, 0) \).
To choose the correct equation that models a specific transformation, we'd need to match the provided options with any specific details of the graph in question.
If the vertex of the graph you’re referring to is at \( (-4, 0) \), then Option A is the correct transformation.
If the vertex has moved to \( (0, 4) \), then it’s Option B.
If the vertex has shifted to \( (4, 0) \), then you should select Option C.
Please clarify which specific transformation or graph you are referring to for the exact match!
1. **Option A: \( y = 2(x + 4)^2 \)**
- This represents a horizontal translation of the graph of \( y = 2x^2 \) to the left by 4 units.
- The vertex of the parabola moves from \( (0,0) \) to \( (-4, 0) \).
2. **Option B: \( y = 2x^2 + 4 \)**
- This represents a vertical translation of the graph of \( y = 2x^2 \) upwards by 4 units.
- The vertex moves from \( (0,0) \) to \( (0, 4) \).
3. **Option C: \( y = 2(x-4)^2 \)**
- This represents a horizontal translation of the graph of \( y = 2x^2 \) to the right by 4 units.
- The vertex moves from \( (0,0) \) to \( (4, 0) \).
To choose the correct equation that models a specific transformation, we'd need to match the provided options with any specific details of the graph in question.
If the vertex of the graph you’re referring to is at \( (-4, 0) \), then Option A is the correct transformation.
If the vertex has moved to \( (0, 4) \), then it’s Option B.
If the vertex has shifted to \( (4, 0) \), then you should select Option C.
Please clarify which specific transformation or graph you are referring to for the exact match!