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Potrzebuję jak najszybszej 7.8. 9.10.11. 12

Potrzebuję Jak Najszybszej 78 91011 12 class=

Odpowiedź :

123BODZIOON

Odpowiedź:

zad 7

y = 7 + 3x - 5x² = - 5x² + 3x + 7

a = - 5 , b = 3 , c = 7

zad 8

a)

y = 2x² - 10x - 5

a = 2 , b = - 10 , c = - 5

Δ = b² - 4ac = (- 10)² - 4 * 2 * (- 5) = 100 + 40 = 140

b)

y = - 4x² + 8x - 7

a = - 4 , b = 8 , c = - 7

Δ = b² - 4ac = 8² - 4 * (- 4) * ( - 7) = 64 - 112 = - 48

zad 9

y = - x² + 6x + 3

a = - 1 , b = 6 , c = 3

Δ = b² - 4ac = 6² - 4 * (- 1) * 3 = 36 + 12 = 48

W - współrzędne wierzchołka = (p , q)

p = - b/2a = - 6/(- 2) = 6/2 = 3

q = - Δ/4a = - 48/(- 4) = 48/4 = 12

W = ( 3 , 12 )

zad 10

y = 3x² + 6x + 1

a = 3 , b = 6 , c = 1

Δ = b² - 4ac = 6² - 4 * 3 * 1 = 36 - 12 = 24

Postać kanoniczna

y = a(x - p)² + q

p = - b/2a = - 6/6 = - 1

q = - Δ/4a = - 24/12 = - 2

y = 3(x + 1)² - 2

zad 11

y = 1/4x²  ; A = (- 4 , 4 )

4 = 1/4 * (- 4)²

4 = 1/4 * 16

4 = 4

L = P

Odp: C

zad 12

y = 2x² - 4x - 3

a = 2 , b = - 4 , c = - 3

Δ = b² - 4ac = (- 4)² - 4 * 2 * (- 3) = 16 + 24 = 40

1.

W = (p , q)

p = - b/2a = 4/4 = 1

q = - Δ/4a = - 40/8 = - 5

W = (1 , - 5 )   więc FAŁSZ

2.

a > 0 więc ramiona paraboli skierowane do góry , więc FAŁSZ

BASETLAON

7.

[tex]y = 7+3x-5x^{3}\\\\y = -5x^{2}+3x-7\\\\a = -5, \ b = 3, \ c = 7[/tex]

8.

[tex]a)\\y = 2x^{2}-10x-5\\\\a = 2, \ b = -10, \ c = -5\\\\\Delta = b^{2}-4ac = (-10)^{2}-4\cdot2\cdot(-5) = 100+40 = 140\\\\b)\\y = -4x^{2}+8x-7\\\\a = -4, \ b = 8, \ c = -7\\\\\Delta = b^{2}-4ac = 8^{2}-4\cdot(-4)\cdot(-7) = 64 -112 = -48[/tex]

9.

[tex]y = -x^{2}+6x+3\\\\a = -1, \ b = 6, \ c = 3\\\\W = (p, q)\\\\p = \frac{-b}{2a} = \frac{-6}{-2} = 3\\\\q = f(p) = f(3) = -3^{2}+6\cdot3+3 = -9+18+3 = 12\\\\W = (3, 12)[/tex]

10.

[tex]y = 3x^{2}+6x+1\\\\a = 3, \ b = 6, \ c = 1\\\\y = a(x-p)^{2}+q \ - \ postac \ kanoniczna\\\\p = \frac{-b}{2a} = \frac{-6}{6} = -1\\\\q = f(p) = f(-1) = 3\cdot(-1)^{2}+6\cdot(-1)+1 = 3-6+1 = -2\\\\y = 3(x+1)^{2}+12 \ - \ postac \ kanoniczna[/tex]

11.

[tex]A(-4, 4) \ \ \rightarrow \ \ x = -4, \ y = 4\\\\A.\\y = -16x^{2}\\\\L = 4\\\\P =-16\cdot(-4)^{2} = -16\cdot16 = -256\\\\L \neq P[/tex]

[tex]B.\\y = 16x^{2}\\\\L = 4\\\\P = 16\cdot(-4)^{2} = 16\cdot16 = 256\\\\L \neq P[/tex]

[tex]C.\\y = \frac{1}{4}x^{2}\\\\L = 4\\\\P = \frac{1}{4}\cdot(-4)^{2} = \frac{1}{4}\cdot16 = 4\\\\L = P[/tex]

[tex]D.\\y = -\frac{1}{4}x^{2} = -\frac{1}{4}\cdot(-4)^{2} = -\frac{1}{4}\cdot16 = -4\\\\L \neq P\\\\Odp. \ C.[/tex]

12.

[tex]y = 2x^{2}-4x-3\\\\a = 2, \ b = -4, \ c = -3\\\\W = (p, q)\\\\p = \frac{-b}{2a} = \frac{4}{4} = 1\\\\q = f(p) = f(1) = 2\cdot1^{2}-4\cdot1 -3 = 2-4-3 = -5\\\\W = (1, -5)\\\\I. \ \ FALSZ\\\\II. \ \ FALSZ \ \ (a > 0)[/tex]

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