Focus, Vertex and Directrix of Parabolas

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What is a parabola?

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A parabola is a symmetric curve formed by the intersection of a cone with a plane parallel to its side. It can be defined as the set of all points that are equidistant from a fixed point (focus) and a fixed line (directrix).

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What is the vertex of a parabola?

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The vertex of a parabola is the point where the parabola changes direction. It is the highest or lowest point on the graph, depending on the orientation of the parabola.

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What is the focus of a parabola?

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The focus of a parabola is a fixed point located inside the curve. It is used in the definition of a parabola, where each point on the parabola is equidistant from the focus and the directrix.

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What is the directrix of a parabola?

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The directrix of a parabola is a fixed line used in the definition of a parabola. Each point on the parabola is equidistant from the focus and the directrix.

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What is the standard form of a vertical parabola?

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What is the standard form of a horizontal parabola?

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How do you find the vertex from the equation of a parabola?

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What does the value of 'p' represent in the parabola's equation?

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The value of 'p' represents the distance from the vertex to the focus (and also from the vertex to the directrix). If p is positive, the parabola opens upwards (or to the right); if negative, it opens downwards (or to the left).

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How can you determine the direction a parabola opens?

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