In the `xy`-plane, the graph of the function `f` defined by `f(x) = x^2 - 6x + 13` is a parabola. A horizontal line wit…

To find the points of intersection, set the expressions for `y` from the two equations equal to each other: `x² - 6x + 13 = 8`. To solve this quadratic equation, first set it equal to zero by subtracting 8 from both sides: `x² - 6x + 5 = 0`. This equation can be factored as `(x - 1)(x - 5) = 0`. The solutions for `x` are `x = 1` and `x = 5`. These are the x-coordinates of the two intersection points. Since both points lie on the horizontal line `y = 8`, the distance between them is the absolute difference of their x-coordinates: `|5 - 1| = 4`.

B is incorrect because it is the value of the larger x-coordinate, not the distance between the two x-coordinates.

C is incorrect because it is the sum of the x-coordinates (`1 + 5 = 6`), not their difference.

D is incorrect because it is the y-coordinate of the intersection points, not the distance between them.