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.

Transformations of Graphs

International Baccalaureate Higher Level Mathematics

2025 HCI P1 Q6

2025 HCI P1 Q6