1, general formula: y = ax 2+bx+cy = ax2+bx+c (a, b, c are constants, aeq0)aeq0).

2. Vertex type: y = a (x-h) 2+ky = a (x? H)2+k(a, h, k are constants, aeq0aeq0).

3. Intersection point (two types): y=a(x-x 1)(x-x2)y=a(x? x 1)(x？ x2)(aeq0aeq0).

4. Standard equation: y {2} = 2pxy2 = 2px.

Parabola, also known as parabola or parabola surface, is a very important concept in mathematics and physics. It originated from the ancient Greek mathematician Archimedes' research on the trajectory of objects under the action of gravity. The shape of parabola is similar to an open bag or a slender water drop. Parabola is widely used in mathematics, physics, engineering and other fields. The mathematical definition of parabola is: let any point on parabola be P(x, y), focus be f and directrix be l.

In physics, parabola is widely used. For example, studying the trajectory of an object under the action of gravity, the object moves along a parabola. When an object falls freely from a static state in a constant gravity field, its trajectory is parabolic. Another example is the trajectory of projectiles in ballistics. When the shell is fired at a certain speed and angle, its flight trajectory is also parabolic.

In the field of engineering, parabola also has important applications. For example, the design of bridges, arches and other buildings often adopts parabolic shape to improve the stability and aesthetics of the structure. In addition, the parabolic shape can also reduce wind resistance and energy consumption. In the field of optics, parabolic reflector is a common optical element, which can focus light on one point and is widely used in telescopes, lasers and other equipment.