1. Über quadratische Ergänzung
f(x) = -2·x^2 + x + 3
f(x) = -2·(x^2 - 1/2·x) + 3
f(x) = -2·(x^2 - 1/2·x + 1/16 - 1/16) + 3
f(x) = -2·(x^2 - 1/2·x + 1/16) + 3 + 1/8
f(x) = -2·(x - 1/4)^2 + 25/8 → S(1/4 | 25/8)
2. Über Formel
f(x) = -2·x^2 + x + 3
Sx = - b/(2·a) = -1/(2·(-2)) = 1/4
Sy = f(Sx) = f(1/4) = -2·(1/4)^2 + (1/4) + 3 = -1/8 + 1/4 + 3 = 25/8 → S(1/4 | 25/8)