Odpowiedź:
a)
y = 3x² - 2x + 1/2
a = 3 , b = - 2 , c = 1/2
Δ = b² - 4ac = (- 2)² - 4 * 3 * 1/2 = 4 - 12/2 = 4 - 6 = - 2
Postać kanoniczna
y = a(x - p)² + q
p = - b/2a = 2/6 = 1/3
q = - Δ/4a = 2/12 = 1/6
y = 3(x - 1/3)² + 1/6
b)
y = - x² + 4x - 8
a = - 1 , b = 4 , c = - 8
Δ = b² - 4ac = 4² - 4 * (- 1) * ( - 8) = 16 - 32 = - 16
Postać kanoniczna
y = a(x - p)² + q
p = - b/2a = - 4/(- 2) = 4/2 = 2
q = - Δ/4a = 16/(- 4) = - 16/4 = - 4
y = - (x - 2)² - 4
