Vertices of an parabola
High School
Definition
The vertices on a parabola refers to the point of maximum curvature. On a parabola there is one vertex located at the highest or lowest point of U bend. The vertex is the midpoint between the focus and directrix.
Worked examples
\(y = x^2 - 4x + 3 = (x - 2)^2 - 1\)
The vertex is at \((2, -1)\), the lowest point of this upward-opening parabola.
\(y = -2(x + 1)^2 + 5\)
Vertex form shows the vertex directly: \((-1, 5)\), the highest point since the parabola opens down.
Common mistakes
- \(y = (x - 3)^2 + 2\) has vertex \((3, -2)\) → vertex is \((3, 2)\) In vertex form \(y = a(x - h)^2 + k\), the vertex is \((h, k)\), not \((h, -k)\).
- Every parabola has multiple vertices → A parabola has exactly one vertex The vertex is the single point of maximum curvature—the tip of the U.
- The vertex is always on the x-axis → The vertex can be anywhere in the plane The vertex y-coordinate depends on the equation; it is not restricted to \(y = 0\).
Where you'll use it next
You'll use the vertex to graph parabolas, solve optimization problems in algebra, and analyze projectile motion and lens focus in physics and calculus.
Found in 1 StudyPug lesson
Conics - Parabola
12th Grade12thGrade 12 Math
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026