Pre-Calculus 11 · Mathematics · Lesson 4.1
Vertex form
- Level
- Grade 11
- Reading time
- 8 min reading
- Review
- Last reviewed 2026-09-03
- Standard
- Accuracy standard
- Errata
Abstract
Graphing parabolas.
What is the vertex form of a quadratic function?
Short answer
Vertex form writes a quadratic as y = a(x − h)² + k, where (h, k) is the vertex of the parabola and a controls its width and direction. If a is positive the parabola opens up (minimum at the vertex); if negative it opens down (maximum). Vertex form makes graphing and finding the maximum or minimum immediate.
Concept preview
What you will be able to do
- 01Recognise a quadratic function and its U-shaped graph, the parabola.
- 02Read the vertex, axis of symmetry, direction of opening, and max/min directly from vertex form .
- 03Explain how , , and transform the base parabola .
- 04Find intercepts, domain, and range from vertex form.
- 05Write the equation of a parabola from its vertex and one other point.
Every graph you have drawn so far has been a straight line — , marching along at one constant slope. A quadratic function is the next rung up the ladder: its highest power is , and that single squared term bends the graph into a smooth, symmetric curve called a parabola. Parabolas are not exotic — they are the exact shape of a thrown ball's flight, the cross-section of a satellite dish or car headlight, the sag of a suspension-bridge cable, and the stream of water from a fountain. Learning to read one equation will let you predict all of that.
School Plan
Vertex form
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Related topics
Frequently asked questions
- What does the vertex tell you?
- It is the highest or lowest point of the parabola — the maximum if it opens down, the minimum if it opens up.
- How do you convert standard form to vertex form?
- By completing the square on the quadratic and linear terms.