Question

wyznacz współrzędne wierzchołka paraboli:

y=(x+4)+8

y=3(x-5)+2

y=-4x-6

y=-2+6x-2

y=2(x+3)(x-7)

y=-3(x+2)(x+4)

Answer 1

WZORY

Δ=b²-4ac

p=-b/2a

q=-Δ/4a

 

a)y=(x+4)²+8

y=x²+8x+16+8

y=x²+8x+24

Δ=8²-4*1*24=64-96=-32

p=-8/2=-4

q=32/4=8

A(-4;8)

 

b)y=3(x-5)²+2

y=3(x²-10x+25)+2

y=3x²-30x+75+2

y=3x²-30x+77

Δ=(-30)²-4*3*77=900-924=-24

p=30/6=5

q=24/12=2

A(5;2)

 

c)y=x²-4x-6

Δ=(-4)²-4*1*(-6)=16+24=40

p=4/2=2

q=-40/4=-8

A(2;-8)

 

d)y=-2x²+6x-2

Δ=6²-4*(-2)*(-2)=36-16=20

p=-6/-4=1½

q=-20/-8=2½

A(1½;2½)

 

e)y=2(x+3)(x-7)

y=2(x²-7x+3x-21)

y=2(x²-4x-21)

y=2x²-8x-42

Δ=(-8)²-4*2*(-42)=64+336=400

p=8/4=2

q=-400/8=-50

A(2;-50)

 

f)y=-3(x+2)(x+4)

y=-3(x²+4x+2x+8)

y=-3(x²+6x+8)

y=-3x²-18x-24

Δ=(-18)²-4*(-3)*(-24)=324-288=36

p=18/-6=-3

q=-36/-12=3

A(-3;3)