РЕШЕНИЕ:

ax² + bx + c = y

K(0; –5) a ∙0 + b ∙ 0 + c = –5 ⇒ c = –5
L(3; 10) a ∙ 3²+ b ∙ 3 + c = 10
M(–3; –2) a ∙( – 3)² + b ∙ ( – 3) + c = – 2

подставим с=–5 во 2 и 3 уравнения

a ∙ 3²+ b ∙ 3 – 5 = 10
a ∙( – 3)² + b ∙ ( – 3) – 5 = – 2

9a + 3b = 15
9a – 3 b = 3

Сложим уравнения

18a = 18
a = 1

9a – 3 b = 3
3a – b = 1
3 – b = 1
b = 2

x₀ = – b/(2a) = – 2/2 = – 1

ax² + bx + c = y

y₀ = 1 ∙ ( – 1)² + 2 ∙ ( – 1) – 5 = 1 – 2 – 5= – 6

Ответ: { – 1 ; – 6}

РЕШЕНИЕ:

ax² + bx + c = y

A(0; 6) a ∙0 + b ∙ 0 + c = 6 ⇒ c = 6
B(6; – 6) a ∙ 6²+ b ∙ 6 + c = – 6
C(1; 9) a ∙1² + b ∙ 1 + c = 9

подставим с=6 во 2 и 3 уравнения

a ∙ 6²+ b ∙ 6 + 6 = – 6
a ∙ 1² + b ∙ 1 + 6 = 9

36a + 6b = – 12
a + b = 3

36a + 6b = – 12
– 6a – 6 b = – 18

Сложим уравнения

30a = – 30
a = – 1

a + b = 3
– 1 + b = 3
b = 4

x₀ = – b/(2a) = – 4/( – 2) = 2

ax² + bx + c = y

y₀ = – 1 ∙ 2² + 4 ∙ 2 + 6 = – 4 + 8 + 6= 10

Ответ: { 2 ; 10}

РЕШЕНИЕ:

ax² + bx + c = y

K(0; –5) a ∙0 + b ∙ 0 + c = – 5 ⇒ c = – 5
L(4; 3) a ∙ 4²+ b ∙ 4 + c = 3
M(–3; 10) a ∙( – 3)² + b ∙ ( – 3) + c = 10

подставим с= – 5во 2 и 3 уравнения

a ∙ 4²+ b ∙ 4 – 5 = 3
a ∙( – 3)² + b ∙ ( – 3) – 5 = 10

16a + 4b = 8 (X 3)
9a – 3b = 15 (X 4)

48a + 12b = 24
36a – 12b = 60

Сложим уравнения

84a = 84
a = 1

16a + 4b = 8
4a + b = 2
4 + b = 2
b = – 2

x₀ = – b/(2a) = 2/2 = 1

ax² + bx + c = y

y₀ = 1 ∙ 1² + ( – 2) ∙ 1 – 5 = 1 – 2 – 5 = – 6

Ответ: { 1 ; – 6}

РЕШЕНИЕ:

ax² + bx + c = y

K(0; –2) a ∙0 + b ∙ 0 + c = – 2 ⇒ c = – 2
L(4; 6) a ∙ 4²+ b ∙ 4 + c = 6
M(1; 3) a ∙6² + b ∙ 6 + c = 3

подставим с= – 2во 2 и 3 уравнения

a ∙ 4²+ b ∙ 4 – 2 = 6
a ∙ 1² + b ∙ 1 – 2 = 3

16a + 4b = 8
a + b = 5

16a + 4b = 8
– 4a – 4b = – 20

Сложим уравнения

12a = – 12
a = – 1

a + b = 5
– 1 + b = 5
b = 6

x₀ = – b/(2a) = – 6/( – 2) = 3

ax² + bx + c = y

y₀ = ( – 1)∙ 3² + 6 ∙ 3 – 2 = – 9 + 18 – 2 = 7

Ответ: { 3 ; 7}

РЕШЕНИЕ:

ax² + bx + c = y

K(0; 2) a ∙0 + b ∙ 0 + c = 2 ⇒ c = 2
L(–5; – 3) a ∙(-5)²+ b ∙ (-5) + c = – 3
M(1; 9) a ∙1² + b ∙ 1 + c = 9

подставим с=2 во 2 и 3 уравнения

a ∙(-5)²+ b ∙ (-5) + 2 = – 3
a ∙1² + b ∙ 1 + 2 = 9

25a – 5b = – 5
a + b = 7

5a – b = – 1
a + b = 7

Сложим уравнения

6a = 6
a = 1

a + b = 7
1 + b = 7
b = 6

x₀ = -b/(2a) = – 6/2 = – 3

ax² + bx + c = y

y₀ = 1∙( –3)² + 6∙( – 3) + 2 = 9 – 18 + 2 = – 7

Ответ: { –3 ; – 7}

РЕШЕНИЕ:

ax² + bx + c = y

A(0; – 6) a ∙0 + b ∙ 0 + c = – 6 ⇒ c = – 6
B(1; – 9) a ∙ 1²+ b ∙ 1 + c = – 9
C(6; 6) a ∙6² + b ∙ 6 + c = 6

подставим с= – 6 во 2 и 3 уравнения

a ∙ 1²+ b ∙ 1 – 6 = – 9
a ∙ 6² + b ∙ 6 – 6 = 6

a + b = – 3
36a + 6b = 12

-6a – 6b = 18
36a + 6b = 12

Сложим уравнения

30a = 30
a = 1

a + b = – 3
1 + b = – 3
b = – 4

x₀ = – b/(2a) = 4/2 = 2

ax² + bx + c = y

y₀ = 1∙ 2² + ( – 4) ∙ 2 – 6 = 4 – 8 – 6 = – 10

Ответ: { 2 ; – 10}