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The Basketball Shot
The Basketball Shot
Maya is practicing basketball shots and notices something interesting about the height of the ball at different time intervals. When she plots the height against time, she gets: 2m, 5m, 10m, 17m, 26m...
At first glance, this doesn't look like a simple pattern. But Maya discovers that this follows a quadratic sequence - a pattern where the differences between differences are constant!
Understanding quadratic sequences helps us model real-world phenomena like projectile motion, falling objects, and growth patterns that accelerate over time.
What are second differences?: The differences between the first differences.
First differences: 4, 6, 8, 10
Second differences: 2, 2, 2
If second differences are constant, the sequence is quadratic.
Mathematics glossary
- What are second differences?
- The differences between the first differences. First differences: 4, 6, 8, 10 Second differences: 2, 2, 2 If second differences are constant, the sequence is quadratic.
- What is a quadratic sequence?
- A sequence where the second differences between consecutive terms are constant. Example: 2, 5, 10, 17, 26, ... First differences: 3, 5, 7, 9, ... Second differences: 2, 2, 2, ... (constant)
Earn the mark scheme marks
Top Tips
- Recognition: If first differences are not constant but second differences are, it's quadratic
- Always check: Substitute values back into your formula to verify it works
- Common mistake: Forgetting that a = ½ × (second difference), not the full second difference
- Pattern tip: Quadratic sequences often involve square numbers, triangular numbers, or growth patterns
- Real-world: Look for quadratic sequences in physics (distance = ½at²), economics (compound interest), and geometry (areas)
- Negative 'a': When a < 0, the sequence eventually decreases (like throwing a ball up)
Now try it yourself
Quiz · Question 1 of 12
Which of the following is a property of a quadratic sequence?
Tap an answer to check it