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Real-World Applications

Part of Quadratic Graphs — GCSE Mathematics

This deep dive covers Real-World Applications 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 9 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 9 of 9

Practice

14 questions

Recall

12 flashcards

Real-World Applications

Physics and Motion

  • Projectile motion: Height of thrown objects
  • Satellite orbits: Parabolic paths
  • Suspension bridges: Cable curves

Business and Economics

  • Profit optimization: Maximum profit calculations
  • Cost minimization: Finding optimal production levels
  • Revenue models: Price vs. demand relationships

Architecture and Design

  • Arch design: Parabolic arches in buildings
  • Dish antennas: Parabolic reflectors
  • Fountains: Water trajectory paths

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.

Transformations of y = x²The 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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