Question

Determine o vértice de cada função abaixo:
a) y = x² -2
b) y = x² - 4x + 13
c) y = 3x² + 8x
d) y = x² - 13
e) y = -x² - 14x - 45
f) y = 6x² + 7x - 5
g) y = -x²+ 2x - 1
h) y = 2x² – 5x + 2
i) y = 2x² - 6x + 5
j) 7 = x² + 4x + 4​

Answer 1

Resposta:

Explicação passo-a-passo:

O Vértice $V(x_v,y_v)$

$x_v=-\frac{b}{2a}\\y_v=-\frac{\Delta}{4*a}$

a) y = x² -2

a=1

b=0

c=-2

Xv= -b/2a

Xv=-0/2*1

Xv=0

---

Yv=-(b²-4*ac)/4*a

Yv= -( -4*1*(-2))/4*1

Yv=-8/4

Yv= -2

V(0,-2)

b) y = x² - 4x + 13

a= 1

b= -4

c= 13

Xv= -(-4)/2*1

Xv=4/2

Xv=2

Yv= -(4²-4*1*13)/4*a

Yv= -(16 -52)/4

Yv= -( -36)/4

Yv=9

V(2,9)

c) y = 3x² + 8x

Xv= -8/2*3

Xv= -8/6

Xv= -4/3

Yv= -(8²)/4*3

Yv=-64/12

Yv= -16/3

V(-4/3 , -16/3)

d) y = x² - 13

Xv=0

Yv= -(-4*1*(-13)/4*1

Yv= - 13

V(0,13)

e) y = -x² - 14x - 45

a= -1

b= -14

c=-45

Xv= -( -14)/2*(-1)

Xv= - 7

Yv= - [(-14)²-4*(-1)*(-45)]/4*(-1)

Yv= - [196-180]/4*(-1)

Yv= -16/4

Yv= -4

V(-7, -4)

f) y = 6x² + 7x - 5

Xv= -7/12

Yv= - [(7²-4*6*(-5))]/4*6

Yv= - [(49+120)]/4*6

Yv= - 169/24

V(-7/12, -169/24)

g) y = -x²+ 2x - 1

Xv= -2/-2

Xv= 1

Yv= -[(4-4*(-1)*(-1)]4*(-1)

Yv= -[(4-4]/4*(-1)

Yv= -0/4*(-1)

Yv=0

V(1,0)

h) y = 2x² – 5x + 2

Xv= -(-5)/2*2

Xv= 5/4

Yv= -(25-4*2*2)/4*2

Yv= -(25-16)/8

Yv= -9/8

V(5/4, -9/8)

i) y = 2x² - 6x + 5

Xv= 6/4

Yv= -(36-4*2*5)/8

Yv= -(-4)/8

Yv=4/8

Yv=1/2

V(6/4,1/2)

j) 7 = x² + 4x + 4​  7?????