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The Trajectory of a Perfect Shot

Part of Quadratic Graphs — GCSE Mathematics

This introduction covers The Trajectory of a Perfect Shot 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 1 of 9 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 9

Practice

14 questions

Recall

12 flashcards

🏹 The Trajectory of a Perfect Shot

Watch a basketball arc through the air, or water flowing from a fountain - these beautiful curved paths follow quadratic graphs! Unlike straight lines, quadratic graphs create elegant parabolas that model everything from projectile motion to profit optimization in business.

The distinctive U-shape (or upside-down U) of quadratic graphs appears everywhere in nature and technology, making them one of the most important mathematical curves to understand.

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 EssentialsQuadratic Graph FeaturesKey Features of 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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