16Hit1600
Advanced MathHardMinimum of a sum of two squared binomials

Advanced Math practice question

What is the minimum value of the function f(x) = (x − 3)² + (x + 1)²?

Answer: 8

Expand: 2x² − 4x + 10 = 2(x − 1)² + 8, which is least, 8, at x = 1. (Directly: f(1) = 4 + 4 = 8.)

Common wrong answers

If you answered 0
0 would need both squares to be 0 at once, which is impossible.
If you answered 1
1 is the x-coordinate of the minimum, not its value.
If you answered 10
10 is f(0), not the minimum.

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