Réponse :
bonjour,
Explications étape par étape
f(x)=4(x-5)²-9
f(x)=4(x²-10x+25)-9
f(x)=4x²-40x+100-9
f(x)=4x²-40x+91
2)
f(x)=4x²-40x+91
Δ=40²-4*4*91
Δ=1600-1456
Δ=144
√Δ=12
x1=(40-12)/8 x1= 28/8 x1=3.5
x2= (40+12)/8 x2= 52/8 x2=6.5
f(x)=4(x-3.5)(x-6.5)
f(x)=2(x-3.5) 2( (x-6.5)
f(x)=( 2x-7)(2x-13)
3)
a) f(x)=0
(2x-7)(2x-13)=0
2x-7=0 2x=7 x=3.5
2x-13=0 2x=13 x= 7.5
b)
f(0)= 0-0+91
f(0)=91
c)
f(x)=-9
4x²-40x+91=-9
4x²-40x+100=0
Δ=40²-4(4)(100)
Δ=1600-1600
Δ=0
x=-b/2a x= 40/8 x=5
f(x)=91
4x²-40x+91=91
4x²-40x+91-91=0
4x²-40x=0
4x(x-10)=0
4x=0 x=0
x-10=0 x=10
f)
minimum
f(x)=ax²+bx+c
si a>0 il existe un minimum
(α;β)
α=-b/2a β=f(α)
4x²-40x+91
α=40/8 α=5
β=f(5) β=4(5²)-40(5)+91 β= 100-200+91 β=-9
