Odpowiedź:
a)
a = 1 , b = 3 , c = - 4
y = x² + 3x - 4
W - współrzędne wierzchołka = (p , q) , gdzie p = - b/2a i q = - Δ/4a
Δ = b² - 4ac = 3² - 4 * 1 * (- 4) = 9 + 16 = 25
p = - b/2a = - 3/2 = - 1 1/2
q = - Δ/4a = - 25/4 = - 6 1/4
W = (- 1 1/2 ; - 6 1/4 )
b)
a = - 2 , b = - 4 , c = 1/2
y = - 2x² - 4x + 1/2
Δ = b² - 4ac = (- 4)² - 4 * (- 2) * 1/2 = 16 + 4 = 20
p = - b/2a = 4/(- 4) = - 4/4 = - 1
q = - Δ/4a = - 20/(- 8) = 20/8 = 5/2 = 2 1/2
W = (- 1 ; 2 1/2 )
c)
a = 1/2 , b = 0 , c = 5
y = 1/2x² + 5
Δ = b² - 4ac = 0² - 4 * 1/2 * 5 = - 10
p = - b/2a = 0/1 = 0
q = - Δ/4a = 10/2 = 5
W = (0 , 5 )
d)
a = - 3 , b =15 , c = 0
y = - 3x² + 15x
Δ = b² - 4ac = 15² - 4 * (- 3) * 0 = 225
p = - b/2a = - 15/(- 6) = 15/6 = 2 3/6 = 2 1/2
q = - Δ/4a = - 225/(- 12) = 225/12 = 18 9/12 = 18 3/4
W = ( 2 1/2 ; 18 3/4)
e)
a = 7 , b = 0 , c = 0
y = 7x²
Δ = b² - 4ac = 0² - 4 * 7 * 0 = 0
p = - b/2a = 0/14 = 0
q = - Δ/4a = 0/28 = 0
W = (0 , 0 )
