Question

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

Answer 1

a)x²-4x-5=0   a=1,b=-4 e c= -5
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)

Answer 2

Ola

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