Vertices are the points, or corners, in geometrical and mathematical shapes where two or more lines meet but do not cross, according to Math Open Reference. Vertices can exist in two-dimensional and three-dimensional shapes. The singular form of vertices is vertex. Sometimes, the term vertex is also used to describe certain points on quadratic equations.
Vertices are often used as a description of the corner of a shape, generally a polygon. However, they can also exist at a point between any two lines which meet and form an angle but do not cross. If the lines cross, the point is considered an intersection and not a vertex. Vertices are a useful way to describe objects and their placement in two-dimensional and three-dimensional spaces. Two-dimensional objects have vertices where their lines meet, and three-dimensional objects have vertices where their planes meet. In this sense, vertices can sometimes be described as the corners of a geometric structure.
In mathematics, the term vertex can also refer to the peak of a parabola. A parabola is a curved shape that is generated by graphically representing a quadratic equation. The peak of a parabola is either the highest or lowest point on the curve, depending on whether it opens upwards or downwards.