Answer
(a) The graph of the equation $y=9-(x-8)^2$ is as shown.
(b) The $x$-intercepts are $(5,0)$ and $(11,0)$.
(c) The solution is $x=5,11$.
(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 $y=9-(x-8)^2$ is as shown.
(b) The $x$-intercepts are $(5,0)$ and $(11,0)$.
(c) Setting $y=0$:
$$0=9-(x-8)^2$$
$$0=9-(x^2-16x+64)$$
$$0=9-x^2+16x-64$$
$$0=-x^2+16x-55$$
$$0=x^2-16x+55$$
$$0=(x-5)(x-11)$$
$$x-5=0$$
$$x=5$$
$$x-11=0$$
$$x=11$$
Thus, the solution is $x=5,11$.
(d) The result from part c is the same as the $x$-intercepts of the graph.
