Question
What is the minimum or maximum point of the graph: y = (x + 6)^2 - 5
Answers
GPT-4o mini
The given equation is \( y = (x + 6)^2 - 5 \). This is a quadratic function in the standard form \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.
1. **Identify the vertex**:
- In this case, the equation is in vertex form: \( y = (x + 6)^2 - 5 \), where:
- \( h = -6 \)
- \( k = -5 \)
- Therefore, the vertex is at the point \( (-6, -5) \).
2. **Determine if it is a minimum or maximum**:
- Since the coefficient of the squared term (which is 1 in this case) is positive, the parabola opens upwards. This means that the vertex represents the minimum point of the graph.
3. **Conclusion**:
- The minimum point of the graph is at \( (-6, -5) \).
1. **Identify the vertex**:
- In this case, the equation is in vertex form: \( y = (x + 6)^2 - 5 \), where:
- \( h = -6 \)
- \( k = -5 \)
- Therefore, the vertex is at the point \( (-6, -5) \).
2. **Determine if it is a minimum or maximum**:
- Since the coefficient of the squared term (which is 1 in this case) is positive, the parabola opens upwards. This means that the vertex represents the minimum point of the graph.
3. **Conclusion**:
- The minimum point of the graph is at \( (-6, -5) \).