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2 years ago

Write the equation of the parabola that has the vertex at point (3,−12) and passes through the point (0,6).

Mathematics

2 answers:

Neporo4naja [7]2 years ago

8 0

Answer:

y = 2(x - 3)² - 12

y = (-4/9)(x - 2)² + 7

Step-by-step explanation:

y = a(x - h)² + k

A) y = a(x - 3)² - 12

6 = a(0 - 3)² - 12

18 = 9a

a = 2

y = 2(x - 3)² - 12

B) y = a(x - 2)² + 7

3 = a(-1 - 2)² + 7

-4 = 9a

a = -4/9

y = (-4/9)(x - 2)² + 7

lana [24]2 years ago

3 0

Answer:

y = 2(x-3)^2 -12

y = -4/9(x-2)^2 +7 bonus

Step-by-step explanation:

The vertex form of a parabola is

y = a(x-h)^2 + k where (h,k) is the vertex

y = a(x-3)^2 - 12

We have one point given (0,6)

6 = a (0-3) ^2 -12

6 = a (-3)^2 -12

6 = 9a-12

Add 12 to each side

6+12 = 9a

18 = 9a

Divide each side by 9

18/9 = 9a/9

a=2

y = 2(x-3)^2 -12

We follow the same steps for the bonus

y = a(x-2)^2 +7

Substitute the point into the equation

3 = a (-1-2)^2 +7

3 =a (-3)^2 +7

3 = 9a +7

subtract 7 from each side

3-7 = 9a +7-7

-4 = 9a

Divide by 9

-4/9 =a

y = -4/9(x-2)^2 +7

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The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. What ar

Degger [83]

Answer:

The minimum value of the bill that is greater than 95% of the bills is $37.87.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 28, \sigma = 6$