Odpowiedź:
a)
f(x) = x² - 6x - 7
x² - 6x - 7 = 0
a = 1 , b = - 6 , c = - 7
Δ = b² - 4ac = (- 6)² - 4 * 1 * (- 7) = 36 + 28 = 64
√Δ = √64 = 8
x₁ = ( - b - √Δ)/2a = ( 6 - 8)/2 = - 2/2 = - 1
x₂ = (- b + √Δ)/2a = (6 + 8)/2 = 14/2 = 7
W - współrzędne wierzchołka = (p , q)
p = - b/2a = 6/2 = 3
q = - Δ/4a = - 64/4 = - 16
Odp: x₀ = { - 1 , 7 } , W = ( 3 , - 16 )
b)
f(x) = 4x² - 4x + 1
4x² - 4x + 1 = 0
a = 4 , b = - 4 , c = 1
Δ = b² - 4ac = (- 4)² - 4 * 4 * 1 = 16 - 16 = 0
x₁ = x₂ = - b/2a = 4/8 = 1/2
W = (p , q)
p = - b/2a = 4/8 = 1/2
q = - Δ/4a = 0/16 = 0
Odp: x₀ = 1/2 , W = (1/2 , 0 )
