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Do parabolas have to be all functions?
No, whether the parabolic opening direction of junior middle school is upward or downward is a function;

But is the parabolic opening in high school left or right? When x takes some values, y has two corresponding values, not a functional relationship.

The trajectory from a plane to a point equal to a fixed straight line is called a parabola. The fixed point is called the focus of parabola, and the fixed straight line is called the directrix of parabola.

A parabola is the trajectory of a point on a plane, which is equal to the distance between the fixed point F (focus) and the fixed point L (directrix). It can be expressed in many ways, such as parameter expression, standard equation expression and so on. It has important applications in geometric optics and mechanics. A parabola is also a conic curve, that is, a conic plane intersects a plane parallel to the generatrix. Parabola can also be regarded as a graph of a quadratic function under appropriate coordinate transformation.

Introduction:

Mathematically, a parabola is a plane curve with mirror symmetry, and it is still a parabola when it roughly points to a U-shape (if it points in different directions). Suitable for any of several obviously different mathematical descriptions, they can all prove to be exactly the same curves.

The description of parabola includes a point (focus) and a line (directrix). It's not about alignment. A parabola is the trajectory of a point on a plane with the same distance from the directrix to the focus. Another description of parabola is a conical section formed by the intersection of a conical surface and a plane parallel to the conical generatrix. The third description is algebra.

The straight line perpendicular to the directrix and passing through the focal point (that is, the straight line passing through the middle decomposition parabola) is called the "symmetry axis". The point on the parabola that intersects the axis of symmetry is called the "vertex", which is the steepest curve point on the parabola. The distance between the vertex and the focus measured along the axis of symmetry is the "focal length".