Parabola

Parabola Class 11 Math
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In math, a parabola is a U-shaped curve that represents the graph of a quadratic function, which is any function that can be written in the form y = ax^2 + bx + c, where a, b, and c are constants, and a is not equal to 0.

Key Properties of Parabolas
Vertex: The highest or lowest point of the parabola, depending on its direction. If a is greater than 0, the parabola opens upward, and the vertex is the minimum point. If a is less than 0, it opens downward, and the vertex is the maximum point.
Axis of Symmetry: A vertical line that passes through the vertex, dividing the parabola into two mirror-image halves. The equation for this line is x = -b/2a.
Focus and Directrix: Every parabola has a point called the focus and a line called the directrix. Points on the parabola are equidistant from the focus and the directrix.

Parabolas appear in many areas of math and physics, such as in projectile motion, where the path of an object follows a parabolic trajectory.

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