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Given \( f(x)=-x^{2}+2 x+8 \), find \( f(-2) \)

Ask by Black Malone. in the United States
Feb 22,2025

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\( f(-2) = 0 \)

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The Deep Dive

To find \( f(-2) \), we simply plug \(-2\) into the function \( f(x) = -x^{2} + 2x + 8 \). Calculating it step by step: 1. Substitute \(-2\) into the function: \[ f(-2) = -(-2)^{2} + 2(-2) + 8 \] 2. Calculate \((-2)^{2}\): \[ (-2)^{2} = 4 \] 3. Substitute that back into the equation: \[ f(-2) = -4 + 2(-2) + 8 \] 4. Calculate \(2(-2)\): \[ 2(-2) = -4 \] 5. Substitute that in: \[ f(-2) = -4 - 4 + 8 \] 6. Combine the terms: \[ f(-2) = -8 + 8 = 0 \] Thus, \( f(-2) = 0 \).

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