Finding X-Intercepts of the Quadratic: y = x(x + 5)

To determine the points of intersection with the x-axis for the function $y = x(x+5)$, follow these steps:

• Step 1: Set the function equal to zero to find the x-intercepts: $y = 0$.
• Step 2: Solve the equation $x(x+5) = 0$.

Considering the product $x(x+5) = 0$:

• If $x = 0$, then one solution is $x = 0$.
• If $x+5 = 0$, then solving for $x$ gives $x = -5$.

Thus, the two points of intersection with the x-axis are:

$(-5, 0)$ and $(0, 0)$.

Therefore, the points of intersection of the function $y = x(x+5)$ with the x-axis are $(-5, 0)$ and $(0, 0)$.