Here are the essential concepts you must grasp in order to answer the question correctly.
Standard Form of a Parabola
The standard form of a parabola that opens vertically is given by the equation (x - h)² = 4p(y - k), where (h, k) is the vertex and p is the distance from the vertex to the focus or directrix. This form allows for easy identification of the parabola's orientation and key features.
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Focus and Directrix
In the context of parabolas, the focus is a fixed point from which distances to points on the parabola are measured, while the directrix is a line that is equidistant from the focus. The parabola is defined as the set of all points that are equidistant from the focus and the directrix, which is crucial for determining its equation.
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Vertex of a Parabola
The vertex of a parabola is the point where it changes direction and is located midway between the focus and the directrix. For the given conditions, the vertex can be calculated as the midpoint of the focus and the directrix, which is essential for writing the standard form of the parabola's equation.
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