Question

Construa os gráficos das seguintes funções, calcule as raízes e o vértice de cada uma.
a) X 2 – 6X – 16 = 0
b) 3x 2 – 9x – 2 = 0
c) – 4x 2 – 5x – 1 = 0

Answer 1

Explicação passo-a-passo:

x²-6x-16=0

A=1

B=-6

C=-16

∆=b²-4ac

∆=(-6)²-4*1*-16

∆=36+64

∆=100

-b±√∆/2a

6±√100/2*1

6±10/2

X¹=6+10/2=16/2=>8

X²=6-10/2=-4/2=>-2

Xv=-b/2a

Xv=6/2*1

Xv=6/2

Xv=3

Yv=-∆/4a

Yv=-100/4*1

Yv=-100/4

Yv=-25

V=>{ 3 e -25}

3x²-9x-2=0

A=3

B=-9

C=-2

∆=b²-4ac

∆=(-9)²-4*3*-2

∆=81+24

∆=105

-b±√∆/2a

9±√105/2*3

9±√105/6

X¹=9+√105/6

X²=9-√105/6

Xv=-b/2a

Xv=9/2*3

Xv=9/6(÷3)

Xv=3/2

Yv=-∆/4a

Yv=-105/4*3

Yv=-105/12(÷3)

Yv=-35/4

V=>{ 3/2 e -35/4}

-4x²-5x-1=0

A=-4

B=-5

C=-1

∆=b²-4ac

∆=(-5)²-4*-4*-1

∆=25-16

∆=9

-b±√∆/2a

5±√9/2*-4

5±3/-8

X¹=5+3/-8=-8/8=>-1

X²=5-3/-8=-2/8(÷2)=>-1/4

Xv=-b/2a

Xv=5/2*-4

Xv=-5/8

Yv=-∆/4a

Yv=-9/4*-4

Yv=-9/-16

Yv=9/16

V=>{-5/8 e 9/16}