A parabola passes through the points and , and its minimum value is . Find the coordinates of the vertex. The vertex is at _________.
Answer & Analysis
Analysis
Question Analysis
This question requires students to use the symmetry property of the parabola to find the axis of symmetry and then determine the vertex coordinates. The minimum value is given, which helps in identifying the ordinate of the vertex.
Key Concept Explanation
The axis of symmetry of a parabola is the vertical line that passes through the vertex. If two points on the parabola have the same y-coordinate, they are symmetric about the axis of symmetry. The abscissa of the vertex is the midpoint of the x-coordinates of these points.
Step-by-step Solution
1. Identify the points and which are symmetric about the axis of symmetry.
2. Calculate the abscissa of the vertex:
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