Determine Intersection Points of y=(x-2)(x+3) with the X-axis

To solve this problem, we'll follow these detailed steps:

• Step 1: Recognize that to find the intersection with the x-axis, we set $y = 0$ for the function $y = (x-2)(x+3)$.
• Step 2: Solve the equation $(x-2)(x+3) = 0$.
• Step 3: Use the zero-product property, which states that if a product equals zero, then at least one of the factors must be zero. Thus:
• $x-2 = 0$ or $x+3 = 0$
• Step 4: Solve each equation:
• For $x-2 = 0$, we add 2 to both sides, yielding $x = 2$.
• For $x+3 = 0$, we subtract 3 from both sides, yielding $x = -3$.
• Step 5: These x-values represent the points of intersection with the x-axis, or the x-intercepts.

Thus, the points of intersection of the function
$y = (x-2)(x+3)$ with the x-axis are the coordinates $(-3,0)$ and $(2,0)$.

Therefore, the solution to the problem is the points $(-3,0),(2,0)$.