11. The table below shows some of the values of \(y = x^2 + x - 4\) for values of \(x\) from –3 to 3.
\(x\)
–3
–2
–1
0
1
2
3
\(y = x^2 + x - 4\)
2
–2
– 4
2
8
(a) Complete the table by finding the values of \(y\) for \(x\) = –1 and for \(x\) = 1. [2]
(b) On the graph paper below, draw the graph of \(y = x^2 + x - 4\) for values of \(x\) from –3 to 3. [2]
(c) Use your graph to solve the equation \(x^2 + x - 4 = 0\). Give your answers correct to 1 decimal place. [1]
\(x =\) ……………………… or \(x =\) ………………………
Mark scheme (a)
Scheme
Marks
Comments
–4 –2
B2
B1 for each
Mark scheme (b)
Scheme
Marks
Comments
At least 5 correct plots and no incorrect plot.
P1
FT ‘their (–1,−4)’ and ‘their (1,−2)’ Allow ± ‘½ a small square’.
A smooth curve drawn through their plots.
C1
FT ‘their 7 plots’ OR a curve through the 5 given points AND (−1,–4) and (1,–2). Allow the intention to pass through their plots (within 1 small square, either horizontally or vertically of the point).
In the original graph the crosses at (−1, −4) and (1, −2) are red and the circles at the x-axis crossings are green.
Mark scheme (c)
Scheme
Marks
Comments
–2·6 AND 1·6
B1
Strict FT ‘their curve’ only if exactly two points of intersection with the \(x\)-axis. Answers must be written to one decimal place. Allow ± ‘up to but not including 1 small square’.
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