2022 ACJC Promo Q3
2022 ACJC Promo Q3
6 marks
Promo
The curve \(C\) with equation \(y=\frac{a{{x}^{2}}+bx+c}{3x+1}\) passes through the point with coordinates \(\left( -1,-4 \right)\) and has a turning point at \(\left( -3,-2 \right)\).
- Find the values of \(a\), \(b\) and \(c\).[3]
- Hence sketch the graph of curve \(C\), stating the equations of any asymptotes and the coordinates of any points where the curve crosses the axes.[3]
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Answer:(i) \(a = 1, b = 0, c = 7\); (ii) OA: \(y = \frac{1}{3}x - \frac{1}{9}\), VA: \(x = -\frac{1}{3}\)
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