The equation y = 2x² – 8x + 9 can be rewritten as y = 2(x – 2)² + 1.To further simplify this equation, you can factor out the 2 from the front to give y = 2(x – 2)(x – 2) + 1. This makes the equation simpler to manipulate and solve for x.
Now, we need to set the equation equal to zero to find the x-intercepts. When y = 0, we have 0 = 2(x – 2)(x – 2) + 1 which can be rewritten as 0 = (x – 2)(x – 2).
To solve this equation, we need to find the roots, or solutions, of the equation. Using the Quadratic Formula, the roots are going to be x = 2 ± √(2² – 4(2)(1)) / 2(2)
This simplifies as x = 2 ± √2 / 4, so our two x-intercepts are x = 0.5 and x = 3.5.
The graph of y = 2(x – 2)² + 1 will have x-intercepts at (0.5, 0) and (3.5, 0). Therefore, the points of intersection of the graph of y = 2(x – 2)² + 1 and the x-axis are (0.5, 0) and (3.5, 0).