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2026 EJC P2 Q3

2026 EJC P2 Q3

Junior College 2
9 marks

A curve \(C\) has equation \(y=\dfrac{5x^2+16x+18}{x^2-4x}\).

  1. State the equations of the asymptotes.[2]
  2. Using an algebraic method, show that \(\dfrac{5x^2+16x+18}{x^2-4x}\) cannot lie between two certain values (to be determined).[4]
  3. Hence sketch the curve \(C\), indicating clearly any turning point(s).[3]

Solution:

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Answer:(a) \(x=0,\ x=4,\ y=5\). (b) \(y\leq-13\) or \(y\geq\frac12\). (c) Local minimum \((-2,\frac12)\); local maximum \((1,-13)\); no axial intercepts.

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