Question

Qual as coordenadas do vertice da parabola das função.

 

a) y=x²-4x-12

 

b)y=x²-6x+9

 

c)y-2x²-5x+2

 

d)y=4x²-9x+2

Answer 1

a) y=x²-4x-12 

Xv= - b/2a ==> xv= -(-4)/2.1 ==> Xv=4/2 ==>Xv= 2

delta= (-4)^2 -4.1.(-12)=16+48=64

Yv= - delta = - 64 ==> Yv = - 16
            4a        4.1
b)y=x²-6x+9 

Xv= - b/2a ==> xv= -(-6)/2.1 ==> Xv=6/2 ==>Xv= 3

delta= (-6)^2 -4.1.9=36-36=0

Yv= - delta = - 0 ==> Yv = 0
            4a      4.1

c)y= -2x²-5x+2 

Xv= - b/2a ==> xv= -(-5)/2.(-2) ==> Xv= - 5/4

delta= (-5)^2 -4.(-2).2=25+16=41

Yv= - delta = - 41 ==> Yv =  41
            4a      4.(-2)               8

d)y=4x²-9x+2

Xv= - b/2a ==> xv= -(-9)/2.4 ==> Xv=9/8 

delta= (-9)^2-4.4.2=81-32=49

Yv= - delta = - 49 ==> Yv = - 49
            4a        4.1                  4