Answer
Zeros: $3,-1$
$x$-intercepts: $3,-1$
Work Step by Step
To find the zeros of a function $g$, solve the equation $g(x)=0$
The zeros of the function are also the $x-$intercepts.
Let $g(x)=0$:
$$(x-1)^2-4=0$$
Using the Square Root Method
$$(x-1)^2=4$$
$$ (x-1) = \pm \sqrt{4}$$
$$(x-1) =\pm 2$$
$\therefore x-1 = 2 \text{ or } x-1 = -2 $
$x-1 = 2 \to x = 3$
$x-1 = -2 \to x =-1$
