The zeros of the functions `f(x)=25-(x+2)^(2)` are

Options

A. `-2 and 5`
B. `-3 and 7`
C. `-5 and 2`
D. `-7 and 3`

Answer

To find the zeros of the function \( f(x) = 25 - (x + 2)^2 \), we need to set the function equal to zero and solve for \( x \).

### Step-by-Step Solution:

1. **Set the function equal to zero**:
\[ f(x) = 0 \implies 25 - (x + 2)^2 = 0 \]

2. **Rearrange the equation**:
\[ (x + 2)^2 = 25 \]

3. **Take the square root of both sides**:
\[ x + 2 = \pm \sqrt{25} \]
Since \( \sqrt{25} = 5 \), we have:
\[ x + 2 = 5 \quad \text{or} \quad x + 2 = -5 \]

4. **Solve for \( x \)**:
- For the first equation:
\[ x + 2 = 5 \implies x = 5 - 2 = 3 \]
- For the second equation:
\[ x + 2 = -5 \implies x = -5 - 2 = -7 \]

5. **Conclusion**:
The zeros of the function are \( x = 3 \) and \( x = -7 \).

### Final Answer:
The zeros of the function \( f(x) = 25 - (x + 2)^2 \) are \( x = 3 \) and \( x = -7 \).