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Transformations of y = x²
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Learn it In y = a(x − h)² + k: |a| > 1 stretches the parabola vertically, 0 < |a| < 1 compresses it, a < 0 reflects it in the x-axis (opens down). h moves it right (left if negative) and k moves it up (down if negative). The vertex is (h, k) and the axis of symmetry is x = h.
Example: Describe y = −2(x + 3)² + 5.
- a = −2: vertical stretch by 2 and a reflection (opens down).
- h = −3: 3 left. k = 5: 5 up.
- Vertex (−3, 5), axis x = −3.
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