A parabola is a curve that looks like the one shown above. Its open end can point up, down, left or right. A curve of this shape is called 'parabolic', meaning 'like a parabola'.
There are three common ways to define a parabola:
In this definition we start with a line (directrix) and a point (focus) and plot the locus of all points equidistant from each. For more see Parabola (focus and directrix).
When we plot the graph of a function of the form the x2 term causes it to be in the shape of a parabola. For more on this see Parabola (Graph of a function).
A parabola is formed at the intersection of a plane and a cone when the plane is parallel to one side of the cone.
See Parabola (Conic section).