Solve the Quadratic Equation: Find Intersection Points of y=(x-2)(x+4)

To solve for the points of intersection of the function $y = (x-2)(x+4)$ with the x-axis, we proceed as follows:

• Set the function equal to zero to find the x-intercepts: $(x-2)(x+4) = 0$.
• Apply the zero-product property, which tells us that if a product of factors equals zero, then at least one of the factors must be zero. Thus, we solve the equations:
• $x-2 = 0$ or $x+4 = 0$.

Solving these equations, we find:

$x-2 = 0$ gives $x = 2$.

$x+4 = 0$ gives $x = -4$.

Therefore, the points of intersection with the x-axis are the points where $y=0$. Substituting these x-values into $y = (x-2)(x+4)$, we confirm that the corresponding y-values are zero:

• For $x = 2$, the point is $(2,0)$.
• For $x = -4$, the point is $(-4,0)$.

Thus, the points of intersection are $(-4,0)$ and $(2,0)$.