Horizontal Parabola: Focus, Directrix, and Vertex
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Conic Sections (Student Workbook)
This example demonstrates a horizontal parabola (an x-type parabola) and how its shape and position change with parameters. It highlights the geometric relationships among the vertex, focus, and directrix. Key mathematical concepts include the definition of a parabola, focus-directrix property, vertex, axis of symmetry, opening direction, focal parameter, and standard equations in coordinate geometry. In the construction, objects a, k, h, and c serve as parameters controlling the curve, while Focus, Directrix, and Vertex are constructed as key objects; text1 is used to display the equation or parameter information. It is suitable for middle-school function graphing, high-school analytic geometry and conic sections, and GeoGebra classroom demonstrations or student exploration.
GeoGebra Commands & Parameters
Numeric a(2.0)Numeric k(1.4679751922668898)Numeric h(1.147866658434528)x = (a * (y - k)^(2)) + h(h + (1 / 4 * a), k)x = h - (1 / 4 * a)(h, k)
AI Drawing Prompt Reference
Draw a horizontal parabola opening to the right, with its vertex at a point on the coordinate plane. The focus is located to the right of the vertex, and the directrix is a vertical line to the left of the vertex. The parabola's shape is controlled by a focal parameter. Label the vertex, focus, and directrix, and display the standard equation of the parabola. Construct the vertex first, then compute the focus and directrix based on the focal parameter, and finally draw the curve.
The prompt above was compiled from the original drawing commands and is for reference only.