Concept guide
Quadratic functions in vertex form: evaluation, symmetry, global maximum and a restricted domain
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.