The curve $y=8+2x-x^2$ meets the line $y=8$ at the positive $x$-coordinate point $A$, and me

Question

The curve $y=8+2x-x^2$ meets the line $y=8$ at the positive $x$-coordinate point $A$, and meets the positive $x$-axis at $B$. Find the coordinates of $A$ and $B$.[3] Hence find the area of the shaded region bounded by the curve, the line and the coordinate axes.[5]

Accepted Answer

(i) $A=(2,8)$, $B=(4,0)$ (ii) $\dfrac{76}{3}\text{ units}^2$

Region with a changing upper boundary

Region with a changing upper boundary

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