For the quadratic function f(x) = x² + 1, find f(−2).
⚠️ Pay close attention to what happens when you square a negative number.
A−3, because (−2)² = −4 and −4 + 1 = −3
B3, because −2 + 1 + 2² = 3
C5, because (−2)² = 4 and 4 + 1 = 5
D−5, because the result of any function at a negative input is negative
Explanation
Substitute x = −2 into f(x) = x² + 1: f(−2) = (−2)² + 1 = 4 + 1 = 5.
The critical step: (−2)² = (−2) × (−2) = +4, NOT −4. A negative times a negative is positive.
Common mistake that gets distractor (A): writing −2² instead of (−2)². Without parentheses, −2² is read by order of operations as −(2²) = −(4) = −4. With parentheses (−2)², you square the negative number itself, giving +4. Always write parentheses around a negative input to a power.