The curve $y=kx-x^2$, where $k0$, meets the positive $x$-axis at $A(4,\ 0)$. Find t

Question

The curve $y=kx-x^2$, where $k>0$, meets the positive $x$-axis at $A(4,\ 0)$. Find the value of $k$.[1] Hence find the area enclosed by the curve and the $x$-axis.[4]

Accepted Answer

(i) $k=4$ (ii) $\dfrac{32}{3}\text{ units}^2$

Parameter from an intercept and the enclosed area

Parameter from an intercept and the enclosed area

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