Question bank / Nonlinear functions

Math · Advanced MathMedium

The function ff is defined by f(x)=x2−6x+13f(x) = x^2 - 6x + 13. What is the minimum value of f(x)f(x)?

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Answer: 4

Complete the square: x2−6x+9+4=(x−3)2+4x^2 - 6x + 9 + 4 = (x - 3)^2 + 4. Since (x−3)2≥0(x - 3)^2 \ge 0, the minimum value is 4, reached at x=3x = 3.

Answering 3 gives the xx-value where the minimum occurs, not the minimum value.

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