Chapter 5 Polynomials and Polynomial Functions - 5.9 Write Polynomial Functions and Models - 5.9 Exercises - Skill Practice - Page 398: 22

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Pick a point $(2,6)$ $y=a(x+3)(x+1)(x)\\ \rightarrow 6=a(2+3)(2+1)(2)\\ \rightarrow 6=30a\\\rightarrow a=\frac{1}{5}$ Hence, the equation will be $y=\frac{1}{5}x(x+3)(x+1)$ $y=a(x+3)(x+1)(x-1)\\ \rightarrow 6=a(2+3)(2+1)(2-1)\\ \rightarrow 6=15a\\\rightarrow a=\frac{2}{5}$ Hence, the equation will be $y=\frac{2}{5}(x+3)(x+1)(x-1)$