Recognise and determine features of the graphs of 𝑦 = 𝑥3, 𝑦 = 𝑎(𝑥 − ℎ)3 + 𝑘 and 𝑦 = 𝑎(𝑥 − 𝑥1)(𝑥 − 𝑥2)(𝑥 − 𝑥3), including shape, intercepts, and behaviour as 𝑥 → ∞ and 𝑥 → − ∞.

mm-u1-t2-s2-d3

Interactive

Cubic graph features

manipulative

Explore shift form a(x−h)³+k and factored form a(x−x₁)(x−x₂)(x−x₃) — opposite end behaviour, inflection, and up to three real roots.

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