To solve for the zeros of the given function $f(x) = (x + 2)^2 - 25$, we set $f(x) = 0$:

$(x + 2)^2 - 25 = 0$

Step 1: Rearrange the equation

$(x + 2)^2 = 25$

Step 2: Solve for $x + 2$

Taking the square root of both sides:

$x + 2 = \pm 5$

This gives two cases:

1. $x + 2 = 5$
2. $x + 2 = -5$

Step 3: Solve for $x$

1. $x + 2 = 5$ → $x = 5 - 2$ → $x = 3$
2. $x + 2 = -5$ → $x = -5 - 2$ → $x = -7$

Final Answer:

The zeros of the function are: $x = -7 \text{ and } x = 3$

This corresponds to option (4): $-7$ and $3$.

Would you like further clarification or details? Here are 5 related questions you can explore:

1. How do transformations of the function $(x + 2)^2 - 25$ affect its graph?
2. What is the significance of the square root step in solving quadratic equations?
3. How do you verify solutions for the zeros of the function?
4. Can this method be generalized for other quadratic equations?
5. How does completing the square relate to solving equations like this?

Tip: Always double-check your solutions by substituting them back into the original equation!