Parabola
The name for the U shaped graph of a quadratic function. It is symmetrical (mirror image)
A parabola is a set of points in a two-dimensional coordinate system that forms a U-shape curve. It is defined as the set of all points that are equidistant to a fixed point (focus) and a fixed line (directrix). The parabola can open upward or downward and can have its vertex at the origin or any point in the coordinate system.
The standard formula for a parabola with the vertex at the origin and opening upward or downward is:
y = ax^2
where a is a nonzero constant that determines the width and direction of the parabola. If the value of a is positive, the parabola opens upward, and if it is negative, the parabola opens downward.
The equation of a horizontal parabola with the vertex at (h,k) is:
(x – h)^2 = 4p(y – k)
where p is the distance from the vertex to the focus or vertex to the directrix. If the value of p is positive, the parabola opens to the right, and if it is negative, the parabola opens to the left.
The equation of a vertical parabola with the vertex at (h,k) is:
(y – k)^2 = 4p(x – h)
where p is the distance from the vertex to the focus or vertex to the directrix. If the value of p is positive, the parabola opens upward, and if it is negative, the parabola opens downward.
Parabolas have many applications in real life, such as in physics to describe the path of a thrown object, in engineering to design reflectors, in architecture to create arches and vaults, and in satellite dish design to focus radio signals.
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