Find the X-Axis Intersections of y = 2x(2x + 4)

To determine the points of intersection of the function $y = 2x(2x+4)$ with the x-axis, we must find where the function equals zero. Such points occur where $y = 0$.

Start by setting the equation to zero:

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

Using the zero-product property, which states that if a product of multiple factors is zero, then at least one of the factors must be zero, we solve as follows:

• Set each factor to zero: $2x = 0$ and $2x + 4 = 0$.
• Solving $2x = 0$: Divide both sides by 2 to get $x = 0$.
• Solving $2x + 4 = 0$: Subtract 4 from both sides to get $2x = -4$, then divide by 2 to get $x = -2$.

Thus, the x-intercepts are at $x = 0$ and $x = -2$.

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

By comparing with the provided multiple-choice options, the correct answer is indeed choice 1: $(-2,0),(0,0)$.