2023 SCSS P1 Q9

2023 SCSS P1 Q9

Secondary 4
8 marks

A curve is such that \(\dfrac{\mathrm d^2y}{\mathrm dx^2}=-3\). The point \((2,-1)\) lies on the curve and the gradient of the curve at this point is 2.

  1. Find the equation of the curve.[6]
  2. Show that the curve does not intersect the \(x\)-axis.[2]

Solution:

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Answer:(i) \(y=-\dfrac32x^2+8x-11\). (ii) Discriminant \(-2<0\).

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