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ozzi
4 years ago
8

Fit a quadratic function to these three points: (-2,8), (0, -4), and (4, 68) Respuesta

Mathematics
1 answer:
zloy xaker [14]4 years ago
3 0

Answer:

f(x) = 4x^2 + 2x - 4.

Step-by-step explanation:

Let the quadratic function be y = f(x) = ax^2 + bx + c.

For the point (-2, 8)  ( x = -2 when y = 8) we have:

a(-2)^2 + (-2)b + c = 8

4a - 2b + c = 8      For (0, -4) we have:

0 + 0 + c = -4   so c = -4.    For (4, 68) we have:

16a + 4b + c = 68  

So we have 2 systems of equations in a and b ( plugging in c = -4):

4a - 2b - 4 = 8

16a + 4b - 4 = 68

4a - 2b = 12

16a + 4b = 72    Multiplying 4a - 2b = 12 by 2 we get:

8a - 4b = 24  

Adding the last 2 equations:

24a = 96

a = 4

Now plugging a = 4 and c = -4 in the first equation:

4(4) - 2b - 4 = 8

-2b = 8 - 16 + 4 = -4

b = 2.

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1 year: $500,000 - 10% * $500,000 = 500,000 - 10/100 * 500,000 = $500,000 - $50,000 = $450,000

2 years: $450,000 - 10% * $450,000 = 450,000 - 10/100 * 450,000 = $450,000 - $45,000 = $405,000

3 years: $405,000 - 10% * $405,000 = 405,000 - 10/100 * 405,000 = $405,000 - $40,500 = $364,500

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The correct result would be $295,000.
6 0
3 years ago
Read 2 more answers
The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with me
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Answer:

218 and 314 days

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 266

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About 99.7% of all pregnancies last between what interval?

Within 3 standard deviations of the mean. So

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