2025 YCKSS PRELIMS P2 Q4

The function is \(y=\dfrac{x}{4}(8-6x+x^2)\).

1. Complete the table, giving the missing value correct to 2 decimal places.[1]

   \(x\)	\(-1\)	\(0\)	\(0.5\)	\(1\)	\(1.5\)	\(2\)	\(2.5\)	\(3\)	\(4\)	\(5\)
   \(y\)	\(-3.75\)	\(0\)		\(0.75\)	\(0.47\)	\(0\)	\(-0.47\)	\(-0.75\)	\(0\)	\(3.75\)

2. Draw the graph for \(-1\leq x\leq5\).[3]
3. Use the graph to solve \(x^3-6x^2+8x=12\) for \(-1\leq x\leq5\).[2]
4. 1. Line \(L\) has gradient \(-0.5\) and passes through \((3,1)\). Draw \(L\) on the same axes for \(-1\leq x\leq5\).[2]
   2. Write the x-coordinate where L intersects the curve.[1]
   3. This x-value solves \(x^3+Ax^2+Bx+C=0\). Find \(A,B,C\).[3]