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Write a quadratic from its zeros, vertex or a family
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Learn it Zeros r and s: y = a(x − r)(x − s). Vertex (h, k): y = a(x − h)² + k. A 'family' shares zeros but has different a-values; one more point fixes a.
Example: Zeros −1 and 5, passing through (2, 18). Find a.
- y = a(x + 1)(x − 5). At x = 2: 18 = a(3)(−3) = −9a.
- a = −2.
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