Question

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

Answer 1

To find \( f(8) \) for the function \( f(x) = -x^2 + 2x + 14 \), we need to substitute \( x = 8 \) into the function.

Let's calculate it step by step:

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

2. Calculate \( 8^2 \):
\[
8^2 = 64
\]

3. Substitute back into the equation:
\[
f(8) = -64 + 2 \cdot 8 + 14
\]

4. Calculate \( 2 \cdot 8 \):
\[
2 \cdot 8 = 16
\]

5. Now substitute this value into the equation:
\[
f(8) = -64 + 16 + 14
\]

6. Combine the values:
\[
f(8) = -64 + 16 = -48
\]
\[
f(8) = -48 + 14 = -34
\]

Thus, the final value is:
\[
f(8) = -34
\]