Answer
(a) The graph of the equation $y=(x+3)^2-4$ is as shown.
(b) The $x$-intercepts are $(-5,0)$ and $(-1,0)$.
(c) The solution is $x=-5,-1$.
(d) The result from part c is the same as the $x$-intercepts of the graph.
Work Step by Step
(a) The graph of the equation $y=(x+3)^2-4$ is as shown.
(b) The $x$-intercepts are $(-5,0)$ and $(-1,0)$.
(c) Setting $y=0$:
$$0=(x+3)^2-4$$
$$0=x^2+6x+9-4$$
$$0=x^2+6x+5$$
$$0=(x+5)(x+1)$$
$$x+5=0$$
$$x=-5$$
$$x+1=0$$
$$x=-1$$
Thus, the solution is $x=-5,-1$.
(d) The result from part c is the same as the $x$-intercepts of the graph.
