Find the Intersection Points of y = (x-2)(x+4) with the X-Axis

The given problem requires us to find the points where the function $y = (x-2)(x+4)$ intersects the x-axis. This is done by determining the values of $x$ that make $y = 0$.

To find these intersection points:

• Set the function equal to zero: $(x-2)(x+4) = 0$.
• Apply the Zero Product Property, which states $(x-2) = 0$ or $(x+4) = 0$.
• Solve each equation:
• $x-2 = 0$ gives $x = 2$.
• $x+4 = 0$ gives $x = -4$.

Thus, the x-coordinates of the intersection points are $x = 2$ and $x = -4$. Since these points represent intersections with the x-axis, their corresponding $y$-coordinates are 0. This gives us the points:

• $(2, 0)$
• $(-4, 0)$

Therefore, the solution to this problem is the points of intersection: $(2, 0)$ and $(-4, 0)$.

Comparing with the answer choices, the correct choice is:

$(2,0),(-4,0)$