Vertex form

Math

Definition

Vertex form is a way of writing a quadratic function as y = a(x − h)² + k, where (h, k) is the vertex of the parabola. This form makes it easy to identify the vertex, axis of symmetry, and direction of opening directly from the equation.

Examples

  • y = 2(x − 3)² + 5 has vertex at (3, 5) and opens upward
  • y = −(x + 1)² − 4 has vertex at (−1, −4) and opens downward
  • Converting y = x² − 6x + 11 to vertex form gives y = (x − 3)² + 2
Key Fact

y = a(x − h)² + k; vertex is (h, k), axis of symmetry is x = h

Related Terms

Completing the square Quadratic formula Parabolas Standard form

Study This Concept

Practice vertex form with free review games in these units:

Algebra 2 Unit 3: Quadratic Functions