Identify which two of graphs A, B, C, D match y = (x − 1)(x − p)(x − q) with q ≥ p and q 1, and state p and q for each chosen graph.

Question

Identify which two of graphs A, B, C, D match y = (x − 1)(x − p)(x − q) with q ≥ p and q > 1, and state p and q for each chosen graph.

Accepted Answer

The coefficient of x³ is +1, so the curve rises to the right: D is ruled out Each graph must cross the x-axis at x = 1 B meets the x-axis only once, but its turning points show it is not a repeated root, so p and q would not be real: B is ruled out A crosses at 1 and touches at 2: roots 1, 2, 2 ⇒ p = 2, q = 2 C crosses at −1, 1, 2 ⇒ p = −1, q = 2 (check y-intercept (−1)(1)(−2) = 2) Answer: Graph A: p = 2, q = 2; Graph C: p = −1, q = 2

0606/23 May/Jun 2026, Question 7: Sketching Cubics and Cubic Inequalities

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