Question

Determine as coodernadas do vértice da parabola que representa cada uma das funções:

a) y= x²+7x+6

Answer 1

x^2 +7x +6

a = 1
b =7
c= 6

X vértice = - b/2a
X vértice = - 7/2.1
X vértice = - 7/2

Y vértice = - delta/4a

Delta = \| b^2 - 4a.c
Delta = \| 7^2 - 4.1.6
Delta = \| 49 - 24
Delta = 5

Y vértice = - 5/4.1
Y vértice = - 5/4

b) y = x^2 - 10x +9

a=1
b= - 10
c= 9

X vértice = - b/2a
X vértice = -(-10)/2.1
X vértice = 10/2
X vértice = 5

Y vértice = - delta/4a

Delta = \| b^2 - 4.a.c
Delta = \| (-10)^2 -4.1.9
Delta = \| 100 - 36
Delta = \| 64
Delta = 8

Y vértice = -8/4.1
Y vértice = - 8/4
Y vértice = - 2

c) y = x^2 + 2x - 8

a = 1
b = 2
c = - 8

Xv = - b/2a
Xv = - 2/2.1
Xv = - 1

Yv = - delta/4a

Delta = \| (b^2) - 4.a.c
Delta = \| 4 - 4.1.(-8)
Delta = \| 4 + 32
Delta = \| 36
Delta = 6

Yv = - 6/4.1
Yv = - 6/4

d) y = x^2 - 2x +1

a = 1
b = - 2
c = 1

Xv = - b/2a
Xv = -(-2)/2.1
Xv = 2/2
Xv = 1

Yv = - delta/4a

Delta = \| (b^2) - 4.a.c
Delta = \| (-2)^2 - 4.1.1
Delta = \| 4-4
Delta = 0

Yv = 0/4.1
Yv = 0

e) y = - x^2 +9

a = - 1
b = 0
c = 9

Xv = - b/2a
Xv = 0/2.1
Xv = 0

Yv = - delta/4a

Delta = \| 0^2 - 4.(-1).9
Delta = \| 36
Delta = 6

Yv = - 6/4.(-1)
Yv = - 6/-4
Yv = 6/4