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Cyberpunk Math Lab: The Non-Linear World FREE

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Quadratic Transformations

55 min Cyberpunk Math Lab: The Non-Linear World

Learning Objectives

  • Understand vertex form
  • Apply transformations
  • Graph parabolas

Key Concepts

Vertex Form

y = a(x - h)² + k where (h, k) is vertex

Transformation

Shift, stretch, or reflect a function

Theory

**Vertex Form: y = a(x - h)² + k** - a: stretch/compress, reflects if negative - h: horizontal shift (opposite sign!) - k: vertical shift **Example:** y = 2(x - 3)² + 1 - Vertex: (3, 1) - Stretch by 2 - Shift right 3, up 1

Examples

Find vertex of y = (x + 2)² - 5

Solution: Vertex: (-2, -5)

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Knowledge Check

Test your understanding of The Ghost Graph!