6. Determine as coordenadas do vertice (x,y) Das funções dadas
a) y=x²-4x-5 b) y=x²+2x-8 c) y=-x²+4x d) y=-x²+4x-3
a) y=x²-4x-5 b) y=x²+2x-8 c) y=-x²+4x d) y=-x²+4x-3
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Δ=b²-4ac
Δ=(-4)²-4.1.(-5)
Δ=16+20
Δ=36
Xv=-b/2a
Xv=-(-4)/2.1
Xv=4/2
Xv=2
Yv=-Δ/4a
Yv=-36/4.1
Yv=-36/4
Yv=-9
(2,-9)
b)x²+2x-8=0 a=1,b=2 e c=-8
Δ=4+32
Δ=36
Xv=-2/2
Xv=-1
Yv=-36/4
Yv=-9
(1,-9)
c)-x²+4x=0
x(-x+4)=0
x=0 ou -x+4=0
-x= -4 (-1)
x=4
Xv= (0+4)/2
Xv=4/2
Xv=2
Yv=-2²+4.2
Yv=-4+8
Yv=4
(2,4)
d)-x²+4x-3=0
Δ=16-12
Δ=4
Xv=-4/(-2)
Xv=2
Yv=-4/(-4)
Yv=2
(2,1)
a)
y = x² - 4x - 5
vértice
Vx = -b/2a = 4/2 = 2
Vy = 2² - 4*2 - 5 = 4 - 8 - 5 = -9
b)
y = x² + 2x - 8
vértice
Vx = -b/2a = -2/2 = -1
Vy = 1 - 2 - 8 = -9
c)
y = -x² + 4x
vértice
Vx = -b/2a = -4/-2 = 2
Vy = -4 + 8 = 4
d)
y = -x² + 4x - 3
vértice
Vx = -b/2a = -4/-2 = 2
Vy = -4 + 8 - 3 = 1