This key facts covers Quadratic Graph Essentials within Quadratic Graphs for GCSE Mathematics. Revise Quadratic Graphs in Graphs for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 2 of 10 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Quadratic Graph Essentials
- General form: y = ax² + bx + c (where a ≠ 0)
- Shape: Parabola (U-shaped curve)
- a > 0: Opens upward (minimum point)
- a < 0: Opens downward (maximum point)
- Vertex: The turning point (minimum or maximum)
- Axis of symmetry: Vertical line through the vertex
Practice questions for Quadratic Graphs
The quadratic y = -3x² + 2x - 1 has a negative coefficient of x². What shape does this parabola make?
Explain how the sign of the coefficient a in y = ax² + bx + c determines the shape of the parabola. Your answer should refer to both cases: a > 0 and a < 0.
Quick recall flashcards
What are the roots of a quadratic graph?
The x-values where the graph crosses the x-axis (where y = 0).
A quadratic can have:
- 2 roots (crosses x-axis twice)
- 1 root (just touches x-axis)
- 0 roots (entirely above or below x-axis)
What is a parabola?
The U-shaped (or n-shaped) curve produced by a quadratic graph.
- a > 0: opens upward (U-shape, minimum)
- a < 0: opens downward (n-shape, maximum)