Question

Determine as coordenadas do vértice da parábola que representa cada função quadrática.
A) y= x² -4 x +3

B) y=-x -6 x -9

C) y = x² +2 x

Answer 1

a) y = x² - 4x + 3
x = -b/2a
x = - (-4)/2.1
x = 4/2
x = 2

Δ = b² -4ac
Δ = (-4)² - 4.(1).(3)
Δ = 16 - 12
Δ = 4

y = -Δ/4a
y = -4/4.1
y = -4/4
y = -1

b) y = -x - 6x - 9

x = -b/2a
x = -(-6)/2.(-1)
x = 6/-2
x = -3

Δ = b² -4ac
Δ = (-6)² - 4.(-1).(-9)
Δ = 36 - 36
Δ = 0

y = -Δ/4a
y = 0/-4
y = 0

c) y = x² + 2x

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

Δ = b² -4ac
Δ = (2)² - 4.(1).(0)
Δ = 4 - 0
Δ = 4

y = -Δ/4a
y = -4/4.1
y = -4/4
y = -1

Answer 2

V(Xv.Yv)

Xv = -b/2a

Yv = -Δ/4a

a) x² - 4x + 3

Xv = -(-4)/2.1 = 4/2 = 2

Yv = -((-4)² - 4(1)(3))/4.1 = -(16 - 12)/4 = -(4)/4 = -4/4 = -1

V(2; -1)

b) -x² -6x - 9

Xv = -(-6)/2(-1) = 6/-2 = -3

Yv = -((-6)² - 4(-1)(-9))/4.(-1) = -(36 - 36)/-4 = 0

V(-3; 0)

c) x² + 2x

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

Yv = -((2)² - 4(1)(0))/4.1 = -(4 - 0)/4 = -4/4 = -1

V(-1; -1)

Espero ter ajudado.