Bonjour
Donner le sommet et les racines :
f(x) = 2x^2 - 8
f(x) = 2(x^2 - 4)
f(x) = 2(x^2 - 2^2)
f(x) = 2(x - 2)(x + 2)
Les racines sont :
x - 2 = 0 ou x + 2 = 0
x = 2 ou x = -2
Le sommet est :
x = -b/2a et y = f(x)
x = -0/(2 * 2) = 0
y = f(0) = 2 * 0^2 - 8 = -8
S = (0 ; -8)
g(x) = -x^2 + 25
g(x) = 25 - x^2
g(x) = 5^2 - x^2
g(x) = (5 - x)(5 + x)
Les racines sont :
5 - x = 0 ou 5 + x = 0
x = 5 ou x = -5
Le sommet est :
x = -b/2a et y = g(x)
x = -0/(2 * -1) = 0
y = g(0) = -1 * 0^2 + 25 = 25
S (0 ; 25)
h(x) = 2(x - 3)(x + 2)
Les racines sont :
x - 3 = 0 ou x + 2 = 0
x = 3 ou x = -2
Le sommet est :
h(x) = 2(x^2 + 2x - 3x - 6) = 2x^2 - 2x - 12
x = -b/2a et y = f(x)
x = 2/(2 * 2) = 2/4 = 1/2
y = h(1/2) = 2 * (1/2)^2 - 2 * 1/2 - 12 = 2 * 1/4 - 2/2 - 12 = 2/4 - 1 - 12 = 1/2 - 13 = 1/2 - 26/2 = -25/2
S (1/2 ; -25/2)
i(x) = -2(x + 1)(x - 5)
Les racines sont :
x + 1 = 0 ou x - 5 = 0
x = -1 ou x = 5
Le sommet est :
i(x) = -2(x^2 - 5x + x - 5) = -2x^2 + 8x + 10
x = -b/2a et y = f(x)
x = -8/(2 * (-2)) = -8/(-4) = 2
y = i(2) = -2 * 2^2 + 8 * 2 + 10 = -2 * 4 + 16 + 10 = -8 + 26 = 18
S (2 ; 18)
