Definition: The common endpoint of two or more
rays
or
line segments

Vertex typically means a corner or a point where lines meet. For example a
square
has four corners, each is called a vertex.
The plural form of vertex is vertices. (Pronounced: "ver - tiss- ease"). A square for example has four vertices.

The word vertex is most commonly used to denote the corners of a
polygon. For examples see:

Vertex is also sometimes used to indicate the 'top' or high point of something,
such as the vertex of an
isosceles triangle
, which is the 'top' corner opposite its base, but this is not its strict mathematical definition.

The lines don't cross.
The two lines that define the vertex meet at their end points. If they cross, the point where they cross is called the
intersection of the two lines.
It is not a vertex.

Solid Geometry

In solid geometry, a vertex is the point where three or more edges meet. In the
cube
below,
one vertex of its possible eight is pointed out. In everyday terms, a vertex of a solid shape is a 'corner'.

A parabola is the shape defined by a quadratic equation.
The vertex is the peak in the curve as shown on the right.
The peak will be pointing either downwards or upwards depending on the sign of the x^{2} term.

For more on quadratic equations and the parabolas they define see
Quadratic Explorer where you can experiment with the
equation and see the effects on the resulting parabola.