The curve $y=(x-1)^2$ intersects the line $y=3-x$ at the points $P$ and $Q$. Find the coordi

Question

The curve $y=(x-1)^2$ intersects the line $y=3-x$ at the points $P$ and $Q$. Find the coordinates of $P$ and $Q$.[3] Hence find the area enclosed by the curve and the line.[4]

Accepted Answer

(i) $P=(-1,4)$, $Q=(2,1)$ (ii) $\dfrac92\text{ units}^2$

Shifted parabola below a descending line

Shifted parabola below a descending line

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