Answer
$-1$
Work Step by Step
The given function is
$\Rightarrow g(x)=-4x^2-8x-4$
Substitute $0$ for $g(x)$.
$\Rightarrow 0=-4x^2-8x-4$
Factor out $-4$.
$\Rightarrow 0=-4(x^2+2x+1)$
Factor the trinomial.
$\Rightarrow 0=-4(x+1)(x+1)$
Use zero product property.
$\Rightarrow x+1=0$ or $x+1=0$
Solve for $x$.
$\Rightarrow x=-1$ or $x=-1$
Hence, the zero of the function is $-1$.
