Answer
The zeros of $f\left( x \right)=-{{\left( x+1 \right)}^{6}}$ are $-1,-1,-1,-1,-1,-1$.
Work Step by Step
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.
