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Quadratic Graph Essentials

Part of Quadratic Graphs — GCSE Mathematics

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 9 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 2 of 9

Practice

14 questions

Recall

12 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

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.

The Trajectory of a Perfect Shot Quadratic Graph Features Key Features of Quadratic Graphs Drawing 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 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)

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The Trajectory of a Perfect Shot

Quadratic Graph Features