Odpowiedź:
1.
a)
y = - 4x² + 6x + 1
a = - 4 , b = 6 , c = 1
Δ = b² - 4ac = 6² - 4 * (- 4) * 1 = 36 + 16 = 52
p = - b/2a = - 6/(- 8) = 6/8 = 3/4
q = - Δ/4a = - 52/(- 16) = 52/16 = 3 4/16 = 3 1/4
Postać kanoniczna
y = a(x - p)² + q = - 4(x - 3/4)² + 3 1/4
b)
y = - 3x² + 4x + 3
a = - 3 , b = 4 , c = 3
Δ = b² - 4ac = 4² - 4 * (- 3) * 3 = 16 + 36 = 52
p = - b/2a = - 4/(- 6) = 4/6 = 2/3
q = - Δ/4a = - 52/(- 12) = 52/12 = 4 4/12 = 4 1/3
Postać kanoniczna
y = a(x - p)² + q = - 3(x - 2/3)² + 4 1/3
2.
a)
y = 2(x - 1)² + 5 = 2(x² - 2x + 1) + 5 = 2x² - 4x + 2 + 5 = 2x² - 4x + 7
y = - 3(x + 4)² + 2 = - 3(x² + 8x + 16) + 2 = - 3x² - 24x - 48 + 2 =
= - 3x² - 24x - 46
b)
y = - 1(x - 2)² + 3 = - (x² - 4x + 4) + 3 = - x² + 4x - 4 + 3 = - x² + 4x - 1
