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Dafna1 [17]
3 years ago
15

The function, f(x) = |x - 2| + 4 has a vertex that is located in which quadrant?

Mathematics
2 answers:
DaniilM [7]3 years ago
8 0
Quadrant one is the answer you should select.
Darina [25.2K]3 years ago
8 0

Answer: Quadrant I

Step-by-step explanation:

The standard equation of the absolute function is given by:

f(x)=|x-h|+k, where (h,k) is the vertex of the absolute function.

The given absolute function : f(x)=|x-2|+4

Comparing to the standard absolute function, the vertex of the given absolute function = (2,4)

Since both the coordinates of the vertex is positive, therefore the vertex lies in Quadrant I .

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Answer:

To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;

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Where we have;

S_{(n)} =  3·4ⁿ + 51

S_{(n+1)} = 3·4ⁿ⁺¹ + 51

S_{(n+1)} - S_{(n)} = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ

S_{(n+1)} - S_{(n)} = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ

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Given that we have for S₀ =  3×4⁰ + 51 = 63 = 9×7

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Since  S_{(n+1)} - S_{(n)} is divisible by 9, we have;

S_{(0+1)} - S_{(0)} =  S_{(1)} - S_{(0)} is divisible by 9

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Step-by-step explanation:

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