In this question you must show detailed reasoning.
Find the coordinates of the points of intersection of the curves with equations \(y = x ^ { 2 } - 2 x + 1\) and \(y = - x ^ { 2 } + 6 x - 5\).
The diagram shows the curves \(y = x ^ { 2 } - 2 x + 1\) and \(y = - x ^ { 2 } + 6 x - 5\).
This diagram is repeated in the Printed Answer Booklet.
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On the diagram in the Printed Answer Booklet, draw the line \(y = 2 x - 2\).
Show on your diagram in the Printed Answer Booklet the region of the \(x - y\) plane within which all three of the following inequalities are satisfied.
\(y \geqslant x ^ { 2 } - 2 x + 1 \quad y \leqslant - x ^ { 2 } + 6 x - 5 \quad y \leqslant 2 x - 2\)
You should indicate the region for which all the inequalities hold by labelling the region \(R\).[1]