Find the $x$-intercept of the graph of $f$.

The graph of $f$ has a maximum at the point A. Write down the coordinates of A.

On the following grid, sketch the graph of $f$.

valid approach     (M1)

eg$\,\,\,\,\,$$f(x) = 0,{\text{ }} \pm 0.816$

0.816496

$x = \sqrt {\frac{2}{3}}$ (exact), 0.816     A1     N2

[2 marks]

$(2.29099,{\text{ }}2.78124)$

${\text{A}}(2.29,{\text{ }}2.78)$     A1A1     N2

[2 marks]

     A1A1A1     N3

Notes:     Award A1 for correct domain and endpoints at $x = 0$ and $x = 7$ in circles,

A1 for maximum in square,

A1 for approximately correct shape that passes through their $x$-intercept in circle and has changed from concave down to concave up between 2.29 and 7.

[3 marks]