Question
What is the minimum or maximum point of the graph: y = (x + 6)^2 - 5
A. Maximum at -5
B. Maximum at -6
C. Minimum at -6
D. Minimum at -5
A. Maximum at -5
B. Maximum at -6
C. Minimum at -6
D. Minimum at -5
Answers
GPT-4o mini
To determine the minimum or maximum point of the graph given by the equation \( y = (x + 6)^2 - 5 \), we can analyze the form of the equation.
The equation \( y = (x + 6)^2 - 5 \) is in the vertex form of a parabola, which is given by \( y = a(x - h)^2 + k \). Here, \( (h, k) \) represents the vertex of the parabola.
1. In this case, \( a = 1 \) (which is positive), indicating that the parabola opens upwards.
2. The vertex of the parabola is at the point \( (-6, -5) \).
Since the parabola opens upwards, the vertex represents the minimum point of the graph.
Therefore, the minimum point of the graph is at \( y = -5 \).
So the correct answer is:
**D. Minimum at -5**
The equation \( y = (x + 6)^2 - 5 \) is in the vertex form of a parabola, which is given by \( y = a(x - h)^2 + k \). Here, \( (h, k) \) represents the vertex of the parabola.
1. In this case, \( a = 1 \) (which is positive), indicating that the parabola opens upwards.
2. The vertex of the parabola is at the point \( (-6, -5) \).
Since the parabola opens upwards, the vertex represents the minimum point of the graph.
Therefore, the minimum point of the graph is at \( y = -5 \).
So the correct answer is:
**D. Minimum at -5**