Solve (x+5)² - 49: Finding X-Axis Intersections

To find the intersection of the function $y = (x+5)^2 - 49$ with the x-axis, we need to solve the equation for $y = 0$.

Set the equation equal to zero:

$(x+5)^2 - 49 = 0$

Add 49 to both sides:

$(x+5)^2 = 49$

Take the square root of both sides, remembering to consider both the positive and negative roots:

$x + 5 = 7$ or $x + 5 = -7$

Solve for $x$ in both cases:

• For $x + 5 = 7$:
  $x = 7 - 5$
  $x = 2$
• For $x + 5 = -7$:
  $x = -7 - 5$
  $x = -12$

Therefore, the x-intercepts of the function are $(-12, 0)$ and $(2, 0)$.

Thus, the function intersects the x-axis at these points.

$(-12, 0), (2, 0)$