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Linear Quadratic Pattern Equations

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Linear Quadratic Pattern Equations

Mathematical patterns and graphs illustration

🎯 WALT: We Are Learning To

• Recognise relationships in linear and quadratic patterns

• Write equations that represent pattern rules

• Use equations and graphs to make mathematical conjectures

📊 Part 1: Pattern Recognition

1. Look at this linear pattern: 3, 7, 11, 15, 19, ...

The rule for this pattern is: y = _______ x + _______

2. Which of these represents a quadratic pattern?

2, 4, 6, 8, 10, ...

1, 4, 9, 16, 25, ...

5, 10, 15, 20, 25, ...

1, 3, 5, 7, 9, ...

3. Complete this table for the pattern y = 2x + 1:

x | 1 | 2 | 3 | 4 | 5

y | __ | __ | __ | __ | __

📈 Part 2: Writing Equations

4. A harakeke (flax) pattern grows like this:

Term 1: 4 leaves, Term 2: 7 leaves, Term 3: 10 leaves, Term 4: 13 leaves

Write the equation for this pattern: y = ______________

5. For the quadratic pattern where y = x² + 2, what are the first 4 terms?

When x = 1: y = ____

When x = 2: y = ____

When x = 3: y = ____

When x = 4: y = ____

6. Match each pattern type to its graph shape:

Linear pattern → Straight line

Quadratic pattern → Curved parabola

Linear pattern → U-shaped curve

Quadratic pattern → Zigzag line

🔍 Part 3: Making Conjectures

7. Look at the pattern: y = 3x² - 1

What do you predict will happen to the y-values as x gets larger?

8. Extension Challenge: Create your own linear pattern starting with 5.

My pattern: 5, _____, _____, _____, _____

My equation: y = ______________

9. Reflection: How can you tell the difference between a linear and quadratic pattern just by looking at the numbers?

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