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Maximum or minimum of a quadratic function

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Useful for: MCR3U MCF3M MBF3C IB Math AA SL & HL

Learn it The vertex of y = ax² + bx + c is at x = −b/(2a). Substitute to get the max (a < 0) or min (a > 0) value. Partial factoring also works: y = x(ax + b) + c has the same value at x = 0 and x = −b/a, so the vertex is halfway.

Example: Find the minimum of y = 2x² − 12x + 5.

  1. x = −(−12)/(2·2) = 3.
  2. y = 2(9) − 36 + 5 = −13, at x = 3.

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