Focal length : The distance between the parabola's vertex and focus.The distance from a parabola's vertex to its directrix is the same as the distance from the parabola's vertex to its focus. Directrix: A line that runs perpendicular to a parabola's axis of symmetry and parallel to its latus rectum.Axis of symmetry: A line that runs through the vertex of a parabola, creating two congruent halves.The distances from the focus and directrix to any point on the hyperbola are the same. Focus : A parabola's focus is a point that is located within the curve of the parabola that the parabola bends around.The vertex form (see Vertex form) can be used to find the vertex of horizontal and vertical parabolas. Vertex : The origin point of a parabola that is located between the directrix and focus.Vertex form of a vertical parabola: if then the vertex is the highest point if then then the vertex is the lowest point.Vertex form of a horizontal parabola:, in which if then the vertex is on the right, and the parabola opens to the left if then the vertex is on the left, and the parabola opens to the right.In the vertex form for both horizontal and vertical parabolas, represents a reflection across the x-axis and/or a vertical stretch or compression, represents a horizontal translation (a shift to the left or right), and represents a vertical translation (a shift up or down). The vertex of a parabola is usually represented by (for the x-coordinate) and (for the y-coordinate), which can be found using the vertex form. Standard form of a vertical parabola: if then the parabola opens downward like a frown if then the parabola opens upward like a smile.
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