Calculate the Intersection Points of the Quadratic Curve y=(x-3)(x+3) and the X-axis

To determine the points of intersection of the function $y=(x-3)(x+3)$ with the x-axis, we need to set $y$ to zero and solve for $x$.

Follow these steps:

• Step 1: Set the function equal to zero: $(x-3)(x+3) = 0$.
• Step 2: Apply the zero-product property, solving each factor for zero:
• For $x-3=0$:

$x = 3$

• For $x+3=0$:

$x = -3$

Thus, the points of intersection of the function with the x-axis, or the x-intercepts, are $(-3, 0)$ and $(3, 0)$.

Therefore, the solution to the problem, confirming x-intercepts, is $(-3, 0), (3, 0)$.