11. The table below shows some of the values of \(y = x^2 - 5x + 2\), for values of \(x\) from −1 to 5.
\(x\)
−1
0
1
2
3
4
5
\(y = x^2 - 5x + 2\)
8
2
−2
−4
−2
2
(a) Complete the table above. [1]
(b) On the graph paper below, draw the graph of \(y = x^2 - 5x + 2\) for values of \(x\) from −1 to 5. [2]
(c) Draw the line \(y = -3\) on the graph paper.
Write down the values of \(x\) where the line \(y = -3\) cuts the curve \(y = x^2 - 5x + 2\). Give your answers correct to 1 decimal place. [2]
Values of \(x\) are ……………… and ………………
Mark scheme (a)
Scheme
Marks
Comments
−4
B1
Mark scheme (b)
Scheme
Marks
Comments
At least 6 correct plots and no incorrect plot.
P1
F.T. ‘their (3,−4)’. Allow ± ‘½ a small square’.
A smooth curve drawn through their plots.
C1
F.T. ‘their 7 plots’. OR a curve through the 6 given points and (3,-4). Allow intention to pass through their plots. (± ‘1 small square horizontal or vertical)’.
Mark scheme (c)
Scheme
Marks
Comments
Line y = −3 drawn
B1
1·4 AND 3·6
B1
F.T. intersection of ‘their curve’ with ‘their y = −3’ only if exactly two points of intersection. Allow ± ‘1 small square’.
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