A-level · Algebra & functions

Transformations of graphsExam-style questions

Moving, stretching and reflecting a graph by changing its equation. Why a change outside the bracket acts on y as written; why a change inside acts on x and works backwards; stretches parallel to the x-axis and their scale factor; the two reflections; tracking a point through a combined transformation; and writing the equation of a transformed curve.

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13 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The curve $y = x^2 - 4x + 7$ is translated by the vector $\begin{pmatrix} 2 \\ -3 \end{pmatrix}$ to give the curve $C$ .
(a) Show that $C$ has equation $y = (x - 4)^2$ . (3 marks)
(b) Write down the coordinates of the vertex of $C$ . (1 mark)
(c) State, with a reason, the number of real roots of the equation $(x - 4)^2 = 0$ , and what this means geometrically for $C$ . (2 marks)
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