Chapter 4 Quadratic Functions and Factoring - 4.9 Graph and Solve Quadratic Inequalities - 4.9 Exercises - Skill Practice - Page 305: 69a

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Let $-x^2+4x=y$ Since the area is bounded below by $y=0$, we have: $-x^2+4x=0\\\rightarrow x^2-4x=0\\ \rightarrow x(x-4)=0\\ \rightarrow x=0 \land x=4$ The base will be $4-0=4$ The axis of symmetry is $x=-\frac{b}{2a}=-\frac{4}{2(-1)}=2$ Substitute back: $y=-(2)^2+4.2=4$ Hence, the area of the region: $A=\frac{2}{3}(4)(4)=\frac{32}{3}\approx 10.667$