# Concept derivation guides

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Concept guide



## [Quadratic functions in vertex form: evaluation, symmetry, global maximum and a restricted domain](/en/derivations/derivation-mko-quadratic-function-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-quadratic-function)

q:ℝ→ℝ, q(x)=−2(x−3)²+5 (a=−2, h=3, k=5). Evaluate q(1) step by step and find its mirror point; prove q(6−x)=q(x) for every real x; prove that the global maximum of q is 5, attained only at x=3, that the vertex is (3,5), and that q has no global minimum; then show that on the restricted domain [4,6] the maximum is 3 (at x=4), and that the conclusions do not carry over when a=0.

Quadratic functions in vertex form

derivation-mko-quadratic-function-01





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