Odpowiedź:
x₁ = - 3 , x₂ = - 1 , P =( - 4 ,6 )
Postać iloczynowa
y = a(x -x₁)(x - x₂) = a(x +3)(x + 1)
6 = a(- 4 + 3)(- 4 + 1) = a *(- 1) * (- 3) =3a
3a = 6
a = 6/3 = 2
y = 2(x +3)(x + 1) = 2(x² + 3x + x + 3) = 2(x² + 4x + 3) = 2x² + 8x + 6
a = 2 , b = 8 , c = 6
Δ = b² - 4ac = 8² - 4 * 2 * 6 = 64 - 48 = 16
Postać kanoniczna
y = a(x - p)² + q
p = - b/2a = - 8/4 = - 2
q = - Δ/4a = - 16/8 = - 2
y = 2(x + 2)² - 2