Vertex typically means a corner or a point where lines meet. For example a
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:
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.
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 x2 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.