Asked by Landon Sharp
Identify the vertex. Is it a maximum or minimum? Reference Sheet - Features of a Parabola (2 points) The vertex is and is a .
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Answered by
GPT-4o mini
To identify the vertex of a parabola and determine whether it is a maximum or minimum, you first need to know the equation of the parabola, which is typically in the form \(y = ax^2 + bx + c\).
1. **Find the Vertex:**
The x-coordinate of the vertex can be found using the formula:
\[
x = -\frac{b}{2a}
\]
Once you have the x-coordinate, substitute it back into the original equation to find the corresponding y-coordinate.
2. **Determine if it is a Maximum or Minimum:**
- If the coefficient \(a\) (from \(y = ax^2 + bx + c\)) is positive, the parabola opens upwards, and the vertex is a **minimum**.
- If \(a\) is negative, the parabola opens downwards, and the vertex is a **maximum**.
If you provide the specific equation of the parabola, I can assist you further in calculating the vertex and identifying if it is a maximum or minimum.
1. **Find the Vertex:**
The x-coordinate of the vertex can be found using the formula:
\[
x = -\frac{b}{2a}
\]
Once you have the x-coordinate, substitute it back into the original equation to find the corresponding y-coordinate.
2. **Determine if it is a Maximum or Minimum:**
- If the coefficient \(a\) (from \(y = ax^2 + bx + c\)) is positive, the parabola opens upwards, and the vertex is a **minimum**.
- If \(a\) is negative, the parabola opens downwards, and the vertex is a **maximum**.
If you provide the specific equation of the parabola, I can assist you further in calculating the vertex and identifying if it is a maximum or minimum.
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