Determine the Intersection Points of y = (x - 9)(x + 7) with the X-Axis

To solve this problem, we'll determine where the function intersects the x-axis by following these steps:

• Step 1: Set the function equal to zero to find the roots.
• Step 2: Solve each factor of the equation independently for $x$.
• Step 3: Confirm the intersection points as the solutions.

Now, let's work through each step:
Step 1: Given the function $y = (x-9)(x+7)$, set $y = 0$ to find the x-intercepts:
$(x-9)(x+7) = 0$.

Step 2: Solve the equation:
The expression $(x-9)(x+7) = 0$ implies that either $x-9 = 0$ or $x+7 = 0$.

Solving each equation:
For $x-9 = 0$, solve for $x$:
$x = 9$.
For $x+7 = 0$, solve for $x$:
$x = -7$.

Step 3: Therefore, the points of intersection are where $y = 0$, which occur at:

The solutions are $x = 9$ and $x = -7$.

The coordinates of these intersection points, given $y = 0$ at each root, are $(-7, 0)$ and $(9, 0)$.

Therefore, the solution to the problem is $(-7, 0), (9, 0)$.