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2 years ago

Pls help, thank you

Mathematics

2 answers:

Lemur [1.5K]2 years ago

8 0

Answer:

y = -3x² + 7x - 9

Step-by-step explanation:

Given quadratic function:

y = ax² + bx + c

Points on the graph:

(-2,-35), (1,-5), (3,- 15)

Substitute values of x and y and solve the system of equations:

-35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c ⇔ eq 1
-5 = a(1)² + b(1) + c ⇒ -5 = a + b + c ⇔ eq 2
-15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c ⇔ eq 3

Subtract eq 2 from eq 1:

-35 - (-5) = 4a - 2b + c - a - b - c
-30 = 3a - 3b
b = a + 10 ⇔ eq 4

Subtract eq 2 from eq 3:

-15 - (-5) = 9a + 3b + c - a - b - c
-10 = 8a + 2b
b = -4a - 5 ⇔ eq 5

Compare eq 4 and eq 5, solve for a:

a + 10 = -4a - 5
a + 4a = -5 - 10
5a = -15
a = -3

Find the value of b using eq 4:

b = -3 + 10
b = 7

Find the value of c using eq 2:

-5 = -3 + 7 + c
c = -5 - 4
c = -9

We now have a, b and c:, the function is:

y = -3x² + 7x - 9

Ronch [10]2 years ago

7 0

Answer:

y = -3x² + 7x - 9

Step-by-step explanation:

Given quadratic function:

y = ax² + bx + c

Points on the graph:

(-2,-35), (1,-5), (3,- 15)

Substitute values of x and y and solve the system of equations:

-35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c ⇔ eq 1

-5 = a(1)² + b(1) + c ⇒ -5 = a + b + c ⇔ eq 2

-15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c ⇔ eq 3

Subtract eq 2 from eq 1:

-35 - (-5) = 4a - 2b + c - a - b - c

-30 = 3a - 3b

b = a + 10 ⇔ eq 4

Subtract eq 2 from eq 3:

-15 - (-5) = 9a + 3b + c - a - b - c

-10 = 8a + 2b

b = -4a - 5 ⇔ eq 5

Compare eq 4 and eq 5, solve for a:

a + 10 = -4a - 5

a + 4a = -5 - 10

5a = -15

a = -3

Find the value of b using eq 4:

b = -3 + 10

b = 7

Find the value of c using eq 2:

-5 = -3 + 7 + c

c = -5 - 4

c = -9

We now have a, b and c:, the function is:

y = -3x² + 7x - 9

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2 years ago

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2 years ago

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2 years ago

Suppose Marcy's rectangular laptop measures 12 inches by 9 inches. Find the diagonal measurement from corner A to corner B.

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Step-by-step explanation:

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Hence the diagonal measurement from corner A to corner B is 15 inches.

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2 years ago

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Answer:

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Step-by-step explanation:

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3 years ago