## Precalculus (6th Edition) Blitzer

The zeros of $f\left( x \right)=-{{\left( x+1 \right)}^{6}}$ are $-1,-1,-1,-1,-1,-1$.
Let’s first equate $f\left( x \right)$ to $0$. So, $-{{\left( x+1 \right)}^{6}}=0$ It can also be written as: $-\left( x+1 \right)\left( x+1 \right)\left( x+1 \right)\left( x+1 \right)\left( x+1 \right)\left( x+1 \right)=0$ So, the zero of the provided function is $x=-1$ with the multiplicity of $6$. The graph touches the x- axis and turns around at $-1$ since it has multiplicity 6. Also, since the function is an even-degree polynomial and the leading coefficient is $-1$, the graph will fall downwards.