Solve (x+3)²-9: Finding X-Axis Intersections of a Shifted Parabola

To solve the problem of finding the intersection of the function $y = (x + 3)^2 - 9$ with the x-axis, we need to set $y = 0$ because the x-axis is defined by $y = 0$.

Starting with the equation:

$(x + 3)^2 - 9 = 0$

Our goal is to solve for $x$. Let's simplify the equation:

Add 9 to both sides:

$(x + 3)^2 = 9$

Next, take the square root of both sides:

$x + 3 = \pm 3$

This gives us two equations to solve:

• $x + 3 = 3$
• $x + 3 = -3$

Solving these equations, we find:

For $x + 3 = 3$:

$x = 0$

For $x + 3 = -3$:

$x = -6$

Thus, the x-intercepts are $(0, 0)$ and $(-6, 0)$. These are the points where the graph intersects the x-axis.

The correct answer, matching the choices given, is choice 3: $(0, 0), (-6, 0)$.