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miss Akunina [59]
3 years ago
11

Using the completing-the-square method, find the vertex of the function f(x) = 5x2 + 10x + 8 and indicate whether it is a minimu

m or a maximum and at what point. (2 points)
Mathematics
1 answer:
jekas [21]3 years ago
5 0
The vertex of the function f(x) = 5x² + 10x + 8 is (-1, 3). the function has a minimum value at 3.

hope this helps, God bless!
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iren [92.7K]

Answer:

  • Part A: The price of fuel A is decreasing by 12% per month.

  • Part B: Fuel A recorded a greater percentage change in price over the previous month.

Explanation:

<u>Part A:</u>

The function     f(x)=2.27(0.88)^x     calculates the price of fuel A each month by multiplying the price of the month before by 0.88.

Month       price, f(x)

1                 2.27 (0.88) = 1.9976 ≈ 2.00

2                2.27(0.88)² = 1.59808 ≈ 1.60

3                2.27(0.88)³ = 1.46063 ≈ 1.46

Then, the price of fuel A is decreasing.

The percentage per month is (1 - 0.88) × 100 = 12%, i.e. the price decreasing by 12% per month.

<u>Part B.</u>

<u>Table:</u>

m       price, g(m)

1          3.44

2         3.30

3          3.17

4         3.04

To find if the function decreases with a constant ration divide each pair con consecutive prices:

  • ratio = 3.30 / 3. 44 = 0.959 ≈ 0.96
  • ratio = 3.17 / 3.30 = 0.960 ≈ 0.96
  • ratio = 3.04 / 3.17 = 0.959 ≈ 0.96

Thus, the price of fuel B is decreasing by (1 - 0.96) × 100 =4%.

Hence, the fuel A recorded a greater percentage change in price over the previous month.

5 0
3 years ago
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