Parabola is like the curve y² = 4 a x .
It is the locus of points which are equidistant from a point called the FOCUS of parabola and a line called DIRECTRIX. The line joining its vertex and focus point is called its axis. The line directrix is perpendicular to the axis.
For the above parabola, y² = 4 a x:
(0,0) is the vertex. (a, 0) is the focus point. Directrix line is x + a = 0
The way to draw the parabola is to first find its vertex, focus, and directrix. Then locate or move point which is equidistant from these two. Start drawing at the vertex and move away from it. In detail: Draw vertex. Choose a point on directrix P'. Join FP'. Find mid-point Q. It lies on y axis. Draw perpendicular bisector for P'F. Draw a horizontal line from P' to meet the bisector at P. P lies on the PARABOLA.
Generally, in Physics: The path of a stone thrown in to the air at an angle is a parabola. Its equation in 2-dimensions is the 2nd order equation in x and y, with some conditions satisfied.
See Diagram for an example.