Given f, of, x, equals, minus, x, squared, plus, 2, x, plus, 14f(x)=−x 
2
 +2x+14, find f, of, 8f(8)

To find \( f(8) \) for the function \( f(x) = -x^2 + 2x + 14 \), we will substitute \( x = 8 \) into the function and compute the result.

### Step-by-Step Solution:

1. **Substitute \( x = 8 \) into \( f(x) \):**
   \[
   f(8) = - (8)^2 + 2 \cdot 8 + 14
   \]

2. **Calculate each term:**

   - \( 8^2 = 64 \)
   - \( -64 = -64 \) (since we have a negative sign before \( x^2 \))
   - \( 2 \times 8 = 16 \)

   So, the expression becomes:
   \[
   f(8) = -64 + 16 + 14
   \]

3. **Combine the terms:**
   \[
   f(8) = -64 + 30 = -34
   \]

### Final Answer:
\[
f(8) = -34
\]

Would you like further details, or do you have any other questions?

### Related Questions:

1. How would you find \( f(-1) \) for the function \( f(x) = -x^2 + 2x + 14 \)?
2. What is the vertex form of the quadratic function \( f(x) = -x^2 + 2x + 14 \)?
3. How do you find the roots of the function \( f(x) = -x^2 + 2x + 14 \)?
4. What is the axis of symmetry for the function \( f(x) = -x^2 + 2x + 14 \)?
5. How would you determine if \( f(x) = -x^2 + 2x + 14 \) has a maximum or minimum value?

**Tip:** Always be careful with negative signs when substituting values into functions, especially for squared terms.

Explore how to calculate f(8) for the quadratic function f(x) = -x^2 + 2x + 14 with a detailed step-by-step solution. Understand the application of the quadratic formula and its usage in solving specific values of functions. Suitable for Grades 9-12.

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