Odpowiedź:
a)
y = x(x - 6)
x(x - 6) = 0
x = 0 ∨ x - 6 = 0
x = 0 ∨ x = 6
x₀ - miejsca zerowe = { 0 , 6 }
y = x(x - 6) = x² - 6x postać ogólna
b)
y = - x(x - 10)
- x(x - 10) = 0
- x = 0 ∨ x - 10 = 0
x = 0 ∨ x = 10
x₀ = { 0 , 10}
y = - x(x - 10) = - x² + 10x postać ogólna
c)
y = 1/2(x + 6)(x - 2)
x + 6 = 0 ∨ x - 2 = 0
x = - 6 ∨ x = 2
x₀ = { - 6 , 2 }
y = 1/2(x + 6)(x - 2) = 1/2(x² + 6x - 2x - 12) = 1/2(x² + 4x - 12) =
= 1/2x² + 2x - 6 postać ogólna
d)
y = - 2(x + 3)(x - 4)
x + 3 = 0 ∨ x - 4 = 0
x = - 3 ∨ x = 4
x₀ = { - 3 , 4 }
y = - 2(x + 3)(x - 4) = - 2(x² + 3x - 4x - 12) = - 2(x² - x - 12) =
= - 2x² + 2x + 24 postać ogólna
e)
y = (2x + 1)(2x - 3)
2x + 1 = 0 ∨ 2x - 3 = 0
2x = - 1 ∨ 2x = 3
x = - 1/2 ∨ x = 3/2 = 1 1/2
x₀ = { - 1/2 ; 1 1/2 }
y = (2x + 1)(2x - 3) = 4x² + 2x - 6x - 3 = 4x² - 4x - 3 postać ogólna
f)
y = (4x - 1)(5 - 4x)
4x - 1 = 0 ∨ 5 - 4x = 0
4x = 1 ∨ - 4x = - 5
x = 1/4 ∨ 4x = 5
x = 1/4 ∨ x = 5/4 = 1 1/4
x₀ = { 1/4 , 1 1/4}
y = (4x -1)(5 - 4x) = 20x - 5 - 16x² + 4x = - 16x² + 24x - 5 postać ogólna
