Parabola
A parabola is a U-shaped curve that is formed by the graph of a quadratic function
A parabola is a U-shaped curve that is formed by the graph of a quadratic function. It is one of the most fundamental curves in mathematics and has several important properties.
The standard equation of a parabola is given by y = ax^2 + bx + c, where a, b, and c are constants. The coefficient a determines whether the parabola opens upwards (a > 0) or downwards (a < 0). The vertex of the parabola is the point (h, k), where h = -b/(2a) and k is the y-coordinate of the vertex. The parabola can also be defined by its geometric shape. It is symmetrical, and the line passing through the vertex is called the axis of symmetry. The focus of the parabola is a fixed point inside the curve, and the directrix is a fixed line outside the curve. The distance from any point on the parabola to the focus is equal to the perpendicular distance to the directrix. This property is known as the focus-directrix property. Parabolas have several applications in the real world. For example, they are used in engineering to design structures with optimal strength and stability. They are also used in physics to describe the trajectory of objects under the influence of gravity. In astronomy, parabolic mirrors are used to focus and reflect light. In summary, a parabola is a U-shaped curve formed by the graph of a quadratic function. It has a vertex, an axis of symmetry, and follows the focus-directrix property.
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