Solve Quadratic Equation x^2 - 9 for X-Axis Intersections

To determine the points of intersection of the function $y = (x+3)(x-3)$ with the x-axis, we need to find the x-values where $y = 0$. These are called the x-intercepts.

We begin by setting the function equal to zero:

$(x+3)(x-3) = 0$

Using the zero-product property, if a product of two terms is zero, then at least one of the factors must be zero. Thus, we set each factor equal to zero and solve for $x$:

• First factor: $x + 3 = 0$
• Solving for $x$, we subtract 3 from both sides:
  $x = -3$
• Second factor: $x - 3 = 0$
• Solving for $x$, we add 3 to both sides:
  $x = 3$

Hence, the solutions for $x$ where $y = 0$ are $x = -3$ and $x = 3$.

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

Comparing with the given answer choices, the correct choice is $(3,0),(-3,0)$.

Therefore, the points of intersection are $(3,0),(-3,0)$.