Determine the Intersection Points of y = x(-x-1) with the X-axis

To solve for the x-intercepts of the function $y = x(-x-1)$, we set $y$ to zero and solve the equation $x(-x-1) = 0$.

Step 1: Identify that the equation is already factored. Set each factor equal to zero:

• $x = 0$
• $-x-1 = 0$

Step 2: Solve for $x$ in each case:
For $x = 0$, the solution is $x = 0$.
For $-x-1 = 0$, add 1 to both sides to get $-x = 1$, then multiply by -1 to find $x = -1$.

Thus, the points of intersection with the x-axis are at $x = 0$ and $x = -1$.

Final Coordinates: Because these are x-intercepts, for both points, the y-coordinate is 0. Therefore, the points of intersection are $(-1, 0)$ and $(0, 0)$.

The correct choice from the given options is $( -1, 0 ), ( 0, 0 )$.