GCSE · Graphs of functions

Transformations of graphs (y = f(x) + a, y = f(x + a), y = −f(x), y = f(−x))Exam-style questions

Move a graph without plotting it again. A number added outside the f moves the curve up or down; a number added inside the bracket moves it sideways, the opposite way to its sign; a minus sign outside reflects it in the x-axis and a minus sign inside reflects it in the y-axis. Track the key points, describe each change fully, combine two changes, write the new equation, and use the same four rules on the sine and cosine waves.

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20 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
$\mathrm{f}(x) = x^2 - 8x + 12$

The graph of $y = \mathrm{f}(x - a) + b$ has its turning point at $(1, 3)$

Find the value of $a$ and the value of $b$ .

You must show all your working.

(4 marks)
Level 5 · 4 marksTry it
2
The curve $C$ has equation $y = x^2 - 10x + 22$
(a) Show that $x^2 - 10x + 22$ can be written as $(x - 5)^2 - 3$

(2 marks)
(b) Write down the coordinates of the turning point of $C$ .

(1 mark)
(c) $C$ is reflected in the $y$ -axis to give the curve $D$ .

Find the equation of $D$ in the form $y = x^2 + px + q$

(2 marks)
(d) Find the exact $x$ -coordinates of the points where $D$ crosses the $x$ -axis.

You must show your working.

(2 marks)
Level 5 · 7 marksTry it
3
The graph of $y = \sin x$ is translated by the vector $\begin{pmatrix} a \\ b \end{pmatrix}$ , where $0 < a < 180$

The translated graph has a minimum point at $(300°, -4)$

Find the coordinates of the point where the translated graph crosses the $y$ -axis.

You must show all your working.

(5 marks)
Level 5 · 5 marksTry it