Find Intersection Points of the Quadratic: y=(-x-3)(x-1) with the X-axis

To solve for the x-intercepts of the function $y = (-x-3)(x-1)$, we need to find where $y = 0$.

The equation becomes:

$(-x-3)(x-1) = 0$

This equation is satisfied if either of the factors equals zero:

• Set the first factor to zero: $-x - 3 = 0$.
  Solve for $x$: $-x = 3$, therefore $x = -3$.
• Set the second factor to zero: $x - 1 = 0$.
  Solve for $x$: $x = 1$.

Thus, the x-intercepts are $(-3, 0)$ and $(1, 0)$.

These correspond with option 3 from the list of choices.

Therefore, the points of intersection of the function with the x-axis are $(1,0),(-3,0)$.