Given that \(b\) is a real constant such that \(0 &lt; b &lt; 4\), describe fully a sequence of transformations that transforms the curve \(y=x^2\) to the curve \(y=4x^2+bx+1\).[4]
Sketch the curve \(y=\frac{1}{4x^2+bx+1}\). Give the equation of any asymptotes and the coordinates of any axial intercepts and turning points, in terms of \(b\) where appropriate.[3]

Given that \(b\) is a real constant such that \(0 < b < 4\), describe fully a sequence of transformations that transforms the curve \(y=x^2\) to the curve \(y=4x^2+bx+1\).

Sketch the curve \(y=\frac{1}{4x^2+bx+1}\). Give the equation of any asymptotes and the coordinates of any axial intercepts and turning points, in terms of \(b\) where appropriate.

2025 HCI P1 Q6

2025 HCI P1 Q6