Question

Do zrobienia 8 zadań

Answer 1

1.

y=-2x² -8x -6

a=-2

b=-8

c=-6

Δ=b²-4ac

Δ=64-48=16

x₁= (-b-√Δ)2a

x₁=(8-4)/-4 = 4/-4 = -1

x₂=(-b+√Δ)/2a

x₂=(8+4)/-4 = 12/-4 = -3

x₀∈{-1;-3}

postac iloczynowa;

y=a(x-x₁)(x-x₂)

y=-2(x+1)(x+3)

postac kanoniczna;

y=a(x-p)²+q

W=(p;q)

p=(x₁+x₂)/2

p=[-1+(-3)]/2=-4/2=-2

q=f(p)=-2(-2+1)(-2+3)=-2

W=(-2;-2)

y=-2(x+2)²-2

2.

a)

(x-2)²+2(3x-4)=6x-8

x²-4x+4+6x-8-6x+8=0

x²-4x+4=0

a=1

b=-4

c=4

Δ=16-16=0

x₀=-b/2a=4/2=2

b)

x⁴-8x-9=0

(x²)²-8x²-9=0

(x²)²-(2√2x)²-3²=0/√

x²-2√2x-3=0

a=1

b=-2√2

c=-3

Δ=8+12=20

3.

a)

(x+2)<2x²+3x+2

-x²+x+2<0/:(-1)

x²-x-2>0

Δ=1+8=9

√Δ=3

x₁=(1-3)/2=-2/2=-1

x₂=(1+3)/2=4/2=2

x₀∈(-∞;-1>u<2;∞)

b)

x²-6x+9≤0

Δ=36-36=0

x₀=-b/2a=6/2=3

x∈{3}

4.

P=a×b

a₁=x

b₁=x+3

P₁=x×(x+3)=x²+3x

a₂=x

b₂=x+3-4

P₂=x×(x-1)=x²-x

P₁=½P₂

2P₁=P₂

2(x²+3x)=(x²-x)

2x²+6x-x²+x=0

x²+7x=0

1.

y=-3x²+6x+9

a=-3

b=6

c=9

Δ=36+108=144

√Δ=12

x₁=(-6-12)/-6=-18/-6=3

x₂=(-6+12)/-6=6/-6=-1

x₀∈{3;-1}

W=(p;q)

p=(x₁+x₂)/2=(3-1)/2=2/2=1

q=f(p)=-3×1²+6×1+9=-3+6+9=12

W=(1;12)

postac iloczynowa;

y=a(x-x₁)(x-x₂)

y=-3(x-3)(x+1)

postac kanoniczna;

y=a(x-p)²+q

y=-3(x-1)²+12

2.

(x+3)²+6x+2=2(3x+1)

x²+6x+9+6x+2-6x-2=0

x²+6x+9=0

a=1

b=6

c=9

Δ=36-36=0

x₀=-b/2a=-6/2=-3

b)

x⁴-3x²-4=0

 

3 .

a)

(x-2)²<2x²-3x-2

x²-4x+4-2x²+3x+2<0

-x²-x+6<0/×(-1)

x²+x-6>0

a=1

b=1

c=-6

Δ=1+24=25

√Δ=5

x₁=(-1-5)/2=-6/2=-3

x₂=(-1+5)/2=4/2=2

x₀={-3;2}

x∈(-∞;-3)u(2;∞)

b)

x²-2x+4≥0

a=1

b=-2

c=4

Δ=4-16=-12

x∈R

4.

Ob.=2km=2000m

e=x

f=x+200

P=(e×f)/2

P=[x×(x+200)]/2=(x²+200x)/2=½x²+100x

Ob.=a×4=2000

a=500

nie cale ale troche pomoglam...;)wiecej nie umiem:(