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2 years ago

Fill out the information below for the following graph of a quadratic function. Please Help!!

Mathematics

1 answer:

Inessa [10]2 years ago

6 0

Answer:

Please refer to the images attached below.

Step-by-step explanation:

Quadratic Functions are functions of degree 2. The graph of any quadratic function is a parabola that has a vertex and axis of symmetry.

Some Properties of Graph Translations

1. y=a(x-h)^2+ky=a(x−h)

This means that the new function is translated h units to the right and k units going up.

2. y=a(x-h)^2-ky=a(x−h)

−k

This means that the new function is translated h units to the right and k units going down.

3. y=a(x+h)^2+ky=a(x+h)

This means that the new function is translated h units to the left and k units going up.

4. y=a(x+h)^2-ky=a(x+h)

−k

This means that the new function is translated h units to the left and k units going down.

First, let's graph the function y=3x^2+3y=3x

+3 . The vertex is at the point (0,3)(0,3) . Please refer to Figure 1 below.

Now, start from the vertex of the first function, (0,3)(0,3) , as you notice that the function y=3(x-3)^2+1y=3(x−3)

+1 is 3 units translation to right and one unit translation going up. This means that the new vertex is the point (3,1)(3,1) .Please refer to Figure 2.

For the function, y=3(x+3)^2-1y=3(x+3)

−1 , start from the vertex of the first function, (0,3)(0,3) , then make a translation of 3 units to the left and a translation of 1 unit down. This gives us a new vertex of (-1, -3)(−1,−3) . Please refer to Figure 3.

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To learn more about quadratic functions, go to

https://brainly.ph/question/2436149

https://brainly.ph/question/4568410

https://brainly.ph/question/5982152

Step-by-step explanation:

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If Upper X overbar equals 62, Upper S equals 8, and n equals 36, and assuming that the population is normally distributed, c

marishachu [46]

Answer:

The 99% confidence interval would be given by (58.373;65.627)

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=62$ represent the sample mean

$\mu$ population mean (variable of interest)

s=8 represent the sample standard deviation

n=36 represent the sample size

Part a: Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=36-1=35$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,35)".And we see that $t_{\alpha/2}=2.72$