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