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Drawing Quadratic Graphs

Part of Quadratic Graphs — GCSE Mathematics

This deep dive covers Drawing Quadratic Graphs 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 5 of 9 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 5 of 9

Practice

14 questions

Recall

12 flashcards

Drawing Quadratic Graphs

Method 1: Table of Values

  1. Choose x-values around the vertex
  2. Calculate y-values using the equation
  3. Plot the points
  4. Join with a smooth curve

Method 2: Key Points

  1. Find the vertex
  2. Find the y-intercept
  3. Find the x-intercepts (if they exist)
  4. Use symmetry to find additional points
  5. Draw smooth curve through all points

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.

Key Features of Quadratic GraphsWorked ExamplesThe Trajectory of a Perfect ShotQuadratic Graph Essentials

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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Key Features of Quadratic Graphs

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Worked Examples