Answer
(a) The graph of the equation $y=(x-5)^2-1$ is as shown.
(b) The $x$-intercepts are $(4,0)$ and $(6,0)$.
(c) The solution is $x=4,6$.
(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 $y=(x-5)^2-1$ is as shown.
(b) The $x$-intercepts are $(4,0)$ and $(6,0)$.
(c) Setting $y=0$:
$$0=(x-5)^2-1$$
$$0=x^2-10x+25-1$$
$$0=x^2-10x+24$$
$$0=(x-4)(x-6)$$
$$x-4=0$$
$$x=4$$
$$x-6=0$$
$$x=6$$
Thus, the solution is $x=4,6$.
(d) The result from part c is the same as the $x$-intercepts of the graph.
