SAT Nonlinear Functions study notes

A nonlinear function can change direction. For quadratics, the vertex tells you where the minimum or maximum occurs. Vertex form a(x − h)² + k makes that visible: when a is positive, the smallest square is zero, so the minimum output is k at x = h.

Worked example

Find the minimum of f(x) = 2x² − 12x + 5.

Complete the square: f(x) = 2(x − 3)² − 13. Since the square cannot be negative, the minimum value is −13, reached at x = 3.

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