Answer:
x = -2 and 4
Explanation:
You want a plot of the x-intercepts of H(x) = (x -1)² -9.
X-intercepts
The x-intercepts are the points where the graph crosses the x-axis, the points where H(x) = 0. Solving, we get ...
H(x) = (x -1)² -9
9 = (x -1)² . . . . . . . . add 9
±3 = x -1 . . . . . take the square root
±3 +1 = x = {-2, 4} . . . . . add 1
Plot
The attached graph shows the coordinates of the x-intercept points on the x-axis. The coordinates of the vertex of the parabola are also shown.