Question

Determine as coordenadas dos vertice de cada funçao :
a) y=x²-8x+16
b) y=2x²+6x
c)y=x²-16

Answer 1

a)x²-8x+16
a=1  b=-8  c=16

Δ=b²-4ac
Δ=(-8)-4.1.16
Δ=64-64
Δ=0

x=-b+-√Δ/2a
x=-(-8)+-√0/2.1
x=8+-0/2

x'=8+0/2 = 8/2 = 4
x''=8-0 = -8/2 = -4

b)2x²+6x   
  a=2 b=6 c=0

Δ=b²-4ac
Δ=(6)²-4.1.0
Δ=36-0
Δ=36

x=-b+-√Δ/2a
x=-6+-√36/2.1
x=-6+-6/2

x'=-6+6/2 = 0/2 = 0
x''= -6-6/2 = -12/2 = -6

c)x²-16
a=1 b=0 c=-16

Δ=b²-4ac
Δ=(0)²-4.1.(-16)
Δ=0+64
Δ=64

x=-b+-√Δ/2a
x=-0+-√64/2.1
x=-0+-8/2

x'=-0+8/2 = 8/2 = 4
x''=-0-8  = -8/2 = -4