A vertex is a corner point where two or more lines, rays, or sides meet. It is the point of an angle, a corner of a polygon such as a triangle, a corner of a solid, and the turning point of a parabola. The plural of vertex is vertices: a square has 4 vertices.
The same word names four kinds of points: where the rays of an angle meet, the corners of a polygon, the corners of a solid, and the turning point of a parabola.
Formal definition and notation
The vertex of an angle is the common endpoint of its two rays. A vertex of a polygon is a point where two adjacent sides meet; a vertex of a polyhedron is a point where three or more edges meet. The vertex of a parabolay = a(x − h)2 + k is the point (h, k), its minimum if a > 0 or maximum if a < 0.
The vertex of a parabola is its turning point; the y-intercept is where it crosses the y-axis. For y = x2 − 6x + 5, the vertex is (3, −4) but the y-intercept is (0, 5).
Quick check: 3 questions
Question 1 of 3
How many vertices does a pyramid with a pentagon base have?
Show answer and explanation
Answer: B. The pentagon base has 5 vertices and the top point (the apex) adds 1: 6 in all. Choice A forgets the apex, and C is the number of edges.
Question 2 of 3
What is the vertex of the parabola y = (x − 4)2 + 7?
Show answer and explanation
Answer: D. In y = a(x − h)2 + k, the vertex is (h, k) = (4, 7): the squared part is 0 when x = 4, leaving y = 7. Choice A takes the wrong sign of h, B swaps the coordinates, and C changes the sign of k.
Question 3 of 3
In ∠ ABC, which point is the vertex?
Show answer and explanation
Answer: C. The vertex is the middle letter, B, where rays BA and BC begin. A and C are points on the rays, and a vertex is a point, not a segment.
Vertex: frequently asked questions
What is the plural of vertex?
The usual plural in math is vertices (VUR-tuh-seez): one vertex, two vertices. Some dictionaries also list vertexes, but textbooks and tests use vertices. The same pattern shows up in index and indices, and in matrix and matrices. Use vertex for a single corner and vertices for two or more.
How do you find the vertex of a parabola?
For y = ax2 + bx + c, the x-coordinate is x = −b2a; substitute it back to find y. For y = 2x2 + 8x + 1, x = −84 = −2 and y = 8 − 16 + 1 = −7, so the vertex is (−2, −7). In vertex formy = a(x − h)2 + k, just read (h, k).
How many vertices does a cube have?
A cube has 8 vertices: 4 around the top face and 4 around the bottom face. It also has 12 edges and 6 faces, and these numbers fit Euler’s formula for solids: V − E + F = 8 − 12 + 6 = 2. A rectangular prism has the same counts.
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