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The Trajectory of a Perfect Shot
🏹 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.
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)
Mathematics glossary
- 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)
Earn the mark scheme marks
💡 Exam Tips for Quadratic Graphs
- Use smooth curves: No sharp corners or straight line segments
- Check the shape: Positive a = smile (∪), negative a = frown (∩)
- Mark key points: Clearly label vertex, intercepts, and any given points
- Use symmetry: If (1, 3) is on the curve and axis is x = 4, then (7, 3) is also on it
- Extend appropriately: Draw curve long enough to show the full parabola shape
- Check by substitution: Verify key points satisfy the equation
Now try it yourself
Quiz · Question 1 of 14
The quadratic y = -3x² + 2x - 1 has a negative coefficient of x². What shape does this parabola make?
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This topic in real past papers
Every real exam question we've found on quadratic graphs, with a full worked answer.