## College Algebra 7th Edition

The $x$-intercepts of the function's graph can be found by equating each factor to zero then solving each equation to obtain: \begin{align*} (x+1)^2&=0 &\text{or}& &(x-1)^3=0& &\text{or}& &x-2=0\\ x+1&=\pm\sqrt0 &\text{or}& &x-1=\sqrt[3]{0}& &\text{or}& &x=2\\ x+1&=0 &\text{or}& &x-1=0\\ x&=-1 \text{ (multiplicity 2) }&\text{or}& &x=1& \\ \end{align*} Thus, the $x$-intercepts are $-1, 1, \text{ and } 2$. The $y$-intercept of the function can be found by setting $x=0$ then solving for $y$: \begin{align*} P(0)&=-(0+1)^2(0-1)^3(0-2)\\ &=-(1^2)(-1)^3(-2)\\ &=-1(-1)(-2)\\ &=-2 \end{align*} Thus, the $y$-intercept is $2$. Create a table of values to obtain the one below. Then, plot each ordered pair and connect the points using a smooth curve. Refer to the graph above.