1 Pure Mathematics
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Question 404
The diagram shows the curve C C\,C with equation y=x2−4x+3y = x^2 - 4x + 3y=x2−4x+3 and the line l l\,l with equation y=2x−2y = 2x - 2y=2x−2.
a.[2]
On the diagram, shade and label the region R R\,R that is satisfied by the inequalities y⩾x2−4x+3y \geqslant x^2 - 4x + 3y⩾x2−4x+3 and y⩽2x−2y \leqslant 2x - 2y⩽2x−2
b.[3]
Determine both common points of C C\,C and lll, giving exact coordinates.
c.[2]
Determine whether the point (2,1)(2, 1)(2,1) lies in RRR, fully justifying your answer.