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3 years ago

Write an equation of the parabola with focus (0, -3) and vertex at the origin. Use z for the independent variable.

Mathematics

1 answer:

olchik [2.2K]3 years ago

4 0

Answer:

z^2 = -12y

or y = -(z^2/12)

Step-by-step explanation:

Answer:

z^2 = -12y

Step-by-step explanation:

Given the vertex at origin;

This is same as (0,0)

The focus (0,-3)

The general form is;

(z-h)^2 = 4p(y-k)

(h,k) is the vertex (0,0); so h = 0 and k = 0

The focus is given as;

(h,k + p)

so ;

k + p = -3

but k =0

so p = -3

Thus, the equation of the parabola is;

(z-0)^2 = 4(-3)(y-0)

z^2 = -12y

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almond37 [142]

Answer:

Step-by-step explanation:

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3 years ago

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Masteriza [31]

Answer:

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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

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Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .