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

Question

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: \[ f(8) = -34 \]