Calculate Intersection Points of Quadratic y = (x-2)(x+4)

Determine the points of intersection of the function

$y=(x-2)(x+4)$

With the X

To solve this problem, we will find the x-intercepts of the function $y = (x-2)(x+4)$.

The function is already in factored form: $y = (x-2)(x+4)$. The x-intercepts occur where $y = 0$.

Set the equation equal to zero:

$(x-2)(x+4) = 0$

Using the Zero Product Property, each factor must equal zero:

• First solve $x - 2 = 0$:
• Add 2 to both sides: $x = 2$
• Next, solve $x + 4 = 0$:
• Subtract 4 from both sides: $x = -4$

The x-intercepts of the function are at points $(2, 0)$ and $(-4, 0)$.

Thus, the points at which the function intersects the x-axis are $(-4,0)$ and $(2,0)$.

Therefore, the correct answer is choice 3: $(-4,0),(2,0)$.