Algebra-1

Question Analysis
This question tests the understanding of the vertex of a parabola and its properties, specifically using symmetry and the given extremum value to find the vertex coordinates.

Key Concept Explanation
The vertex of a parabola is the point where the parabola reaches its maximum or minimum value. For a parabola that opens upwards, the vertex is the lowest point, and for a parabola that opens downwards, the vertex is the highest point. The axis of symmetry of the parabola passes through the vertex.

Step-by-step Solution
1. Identify the symmetric points: The points and are symmetric about the axis of symmetry.
2. Calculate the axis of symmetry: The axis of symmetry is the vertical line passing through the midpoint of the x-coordinates of the symmetric points. Thus,

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