Question
Question 4 A)Match the equation with its feature.(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. y=−2(x+3)2−7y=−2(x+3)2−7 y=(x+7)2−3y=(x+7)2−3 y=12(x+3)2−7y=12(x+3)2−7 y=(x−3)2+7y=(x−3)2+7 Axis of Symmetry is x=−7x=−7Maximum at −7−7Vertex at (3, 7)Minimum at −7−7
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GPT-4o mini
To match the equations with their corresponding features, we first analyze each equation provided:
1. **y = −2(x+3)²−7**
- **Axis of Symmetry**: x = -3 (since it is derived from (x+3)²)
- **Vertex**: (-3, -7)
- **Maximum/Minimum**: Since the coefficient of the squared term is negative, it opens downwards, indicating a maximum.
2. **y = (x+7)²−3**
- **Axis of Symmetry**: x = -7 (since it is derived from (x+7)²)
- **Vertex**: (-7, -3)
- **Maximum/Minimum**: Since the coefficient of the squared term is positive, it opens upwards, indicating a minimum.
3. **y = 12(x+3)²−7**
- **Axis of Symmetry**: x = -3 (since it is derived from (x+3)²)
- **Vertex**: (-3, -7)
- **Maximum/Minimum**: Since the coefficient of the squared term is positive, it opens upwards, indicating a minimum.
4. **y = (x−3)²+7**
- **Axis of Symmetry**: x = 3 (since it is derived from (x−3)²)
- **Vertex**: (3, 7)
- **Maximum/Minimum**: Since the coefficient of the squared term is positive, it opens upwards, indicating a minimum.
Now matching these equations with the provided features:
### Matches
- **Equation:** y = (x + 7)² - 3
- **Axis of Symmetry:** x = -7
- **Vertex:** (-7, -3)
- **Maximum at:** N/A (it is a minimum)
- **Equation:** y = (x - 3)² + 7
- **Vertex at:** (3, 7)
- **Maximum at:** N/A (it is a minimum)
- **Equation:** y = 12(x + 3)² - 7
- **Minimum at:** -7 (indicates a vertex)
- **Equation:** y = -2(x + 3)² - 7
- **Maximum at:** -7 (indicates a vertex)
Now you can input the matched pairs based on the explanation above.
1. **y = −2(x+3)²−7**
- **Axis of Symmetry**: x = -3 (since it is derived from (x+3)²)
- **Vertex**: (-3, -7)
- **Maximum/Minimum**: Since the coefficient of the squared term is negative, it opens downwards, indicating a maximum.
2. **y = (x+7)²−3**
- **Axis of Symmetry**: x = -7 (since it is derived from (x+7)²)
- **Vertex**: (-7, -3)
- **Maximum/Minimum**: Since the coefficient of the squared term is positive, it opens upwards, indicating a minimum.
3. **y = 12(x+3)²−7**
- **Axis of Symmetry**: x = -3 (since it is derived from (x+3)²)
- **Vertex**: (-3, -7)
- **Maximum/Minimum**: Since the coefficient of the squared term is positive, it opens upwards, indicating a minimum.
4. **y = (x−3)²+7**
- **Axis of Symmetry**: x = 3 (since it is derived from (x−3)²)
- **Vertex**: (3, 7)
- **Maximum/Minimum**: Since the coefficient of the squared term is positive, it opens upwards, indicating a minimum.
Now matching these equations with the provided features:
### Matches
- **Equation:** y = (x + 7)² - 3
- **Axis of Symmetry:** x = -7
- **Vertex:** (-7, -3)
- **Maximum at:** N/A (it is a minimum)
- **Equation:** y = (x - 3)² + 7
- **Vertex at:** (3, 7)
- **Maximum at:** N/A (it is a minimum)
- **Equation:** y = 12(x + 3)² - 7
- **Minimum at:** -7 (indicates a vertex)
- **Equation:** y = -2(x + 3)² - 7
- **Maximum at:** -7 (indicates a vertex)
Now you can input the matched pairs based on the explanation above.
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