The graph of the equation x2 + y = 0 intersects the x-axis where the value of y is equal to zero. To find these intersection points, we can set y to zero and solve for x.
Start with the equation:
x2 + y = 0
Setting y = 0 gives us:
x2 + 0 = 0
This simplifies to:
x2 = 0
Solving for x, we take the square root of both sides:
x = 0
Therefore, the graph crosses the x-axis at the point (0, 0). This point is the only point of intersection because the equation represents a parabola that opens upwards, meaning it will not cross the x-axis at any other point.
In conclusion, the graph of x2 + y = 0 intersects the x-axis at the origin, or (0, 0).