Find the X-Intercepts of the Quadratic: y=x(x-1)

Consider the following function:

$y=x(x-1)$

Determine the points of intersection with x.

To solve this problem, we'll need to determine where the function intersects the x-axis, which occurs where $y = 0$.

Let's work through the solution:

• Step 1: Set the function equal to zero: $x(x-1) = 0$.
• Step 2: Apply the zero-product property, which states that if the product of two numbers is zero, at least one of the factors must be zero.
• Step 3: Set each factor equal to zero: $x = 0$ or $x - 1 = 0$.
• Step 4: Solve for $x$ in each equation:
  - For $x = 0$: This immediately gives us the solution $x = 0$.
  - For $x-1 = 0$: Add 1 to both sides to get $x = 1$.

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

This matches with choice 2, thus confirming the correct option.

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