Vertex

High School

Definition

Vertex refers to one point where two edges or lines meet. The plurl form is "vertices." In geometry, it is the corner points of the shape. In an angle, the vertex is the endpoint where two lines begin or meet. In three dimentional solids, the vertex refers to the point where three or more lines meet up. On a curve with no corners, the vertex refers to the point of maximum curvature (bends the most).

Worked examples

\(\)In triangle \( ABC\), points \( A, B, \) and \( C \) are the three vertices.\(\)

Each corner where two edges meet is a vertex of the polygon.

\(\)In angle \( \angle DEF\), point \( E \) is the vertex.\(\)

The vertex of an angle is the endpoint where the two rays meet.

\(\)The parabola \( y = x^2 \) has its vertex at \( (0, 0).\)

On a parabola, the vertex is the turning point where the curve bends the most.

Common mistakes

\(\)Calling any point on the edge a vertex\(\) → \(\)Only corner points where edges meet are vertices\(\) A vertex must be where two or more edges or lines meet, not just any point on the shape.
\(\)Saying "vertexes" for the plural\(\) → \(\)The plural is "vertices"\(\) The correct mathematical plural of vertex is vertices, not vertexes.
\(\)Confusing the vertex of a parabola with its \( x\)-intercepts\(\) → \(\)The vertex is the turning point, not where it crosses the \( x\)-axis\(\) The vertex is the maximum or minimum point; intercepts are where the graph crosses an axis.

Where you'll use it next

You'll use vertices when naming polygons and solids in geometry, finding turning points of parabolas in algebra, solving optimization problems in calculus, and working with graphs and networks in discrete math.

Found in 1 StudyPug lesson

Quadratic function in vertex form: <i>y = a(x-p)^2 + q</i>

College Algebra

Besides the general form, the vertex form is also another way to express a quadratic function. In this lesson, we will talk about how to find the x-intercepts, y-intercepts, vertex of quadratic functions in vertex form.

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