Find X-Axis Intersections of y=(x+3)² : Quadratic Function Analysis

To solve this problem, we will follow these steps:

• Step 1: Identify the function as $y = (x+3)^2$.
• Step 2: Set $y = 0$ to find the intersection with the x-axis.
• Step 3: Solve $(x+3)^2 = 0$ to find the x-coordinate.

Let's proceed through each step:
Step 1: We are given the function $y = (x+3)^2$.
Step 2: To find where this function intersects the x-axis, set $y = 0$:

$(x+3)^2 = 0$

Step 3: Solve the equation:
The equation $(x+3)^2 = 0$ suggests that $x+3 = 0$,
which simplifies to $x = -3$.

Therefore, the intersection point is where $x = -3$ and $y = 0$, giving us the intersection at $(-3, 0)$.

Thus, the solution to the problem is $(-3, 0)$, corresponding to choice given as $(-3, 0)$.