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Quadratic Graph Features

Part of Quadratic Graphs · GCSE GCSE Mathematics revision

This diagram covers Quadratic Graph Features 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 3 of 10 in this topic. Focus on the labels, the relationships between parts, and the explanation that turns the diagram into an exam-ready answer.

Topic position

Section 3 of 10

Practice

14 questions

Recall

12 flashcards

Quadratic Graph Features

Vertex (2, -1) Minimum point x = 2 axis of symmetry (0, 3) y-intercept (1, 0) (3, 0) x-intercepts (roots) y = x² - 4x + 3 a = 1 (positive, opens upward) Vertex: (2, -1) Roots: x = 1, x = 3 y x 0 1 2 3 1 2 3

Keep building this topic

Read this section alongside the surrounding pages in Quadratic Graphs. That gives you the full topic sequence instead of a single isolated revision point.

Quadratic Graph EssentialsKey Features of Quadratic GraphsThe Trajectory of a Perfect ShotDrawing Quadratic Graphs

Practice Questions for Quadratic Graphs

The quadratic y = -3x² + 2x - 1 has a negative coefficient of x². What shape does this parabola make?

  • A. U-shape (opens upward, minimum point)
  • B. ∪-shape (opens upward, minimum point at top)
  • C. ∩-shape (opens downward, maximum point)
  • D. S-shape (neither minimum nor maximum)
1 markfoundation

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.

2 marksstandard

Quick Recall Flashcards

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)
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)

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Quadratic Graph Essentials

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Key Features of Quadratic Graphs