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2 years ago

How are the coordinates of the extreme value and the equation from part B in the form y=(x-h)^2-c related.

Mathematics

1 answer:

True [87]2 years ago

4 0

The extreme value of y = (x - h)² - c is the vertex of the equation.

<h3>What are extreme values of a function?</h3>

The extreme values of a function are either the maximum or minimum values of the function.

<h3>The equation of a parabola in vertex form</h3>

The equation of a parabola in vertex form with vertex (h', k) is given by

y = a(x - h')² + k and its extreme values are

if a > 0 (h', k) is a minimum point and
if a < 0 (h', k) is a maximum point.

Since y = (x - h)² - c is the equation of a parabola in vertex form, comparing with y = a(x - h')² + k,

h = h'
-c = k and
a = 1.

So, the cooordinates of the vertex of y = (x - h)² - c is (h, -c).

Now, since a = 1 > 0, (h, -c) is a minimum point.

So, the extreme value of y = (x - h)² - c is the vertex of the equation.

Learn more about extreme value of a function here:

brainly.com/question/13464558

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You might be interested in

A school chorus has 90 sixth-grade students and 75 seventh-grade students. The music director wants to make groups of performers

Vera_Pavlovna [14]

Answer:

a) 15 is the largest number of groups that can be made.

b) There would 6 sixth grade students and 5 seventh grade students in each group.

Step-by-step explanation:

Number of sixth-grade students = 90

Number of seventh-grade students = 75

a) What is the largest number of groups that could be formed?

Since the music director wants to make groups with the same combination of sixth and seventh grade students in each group,

The greatest common factor (GCF) of the number of sixth and seventh grade students would give us the required combination.

Factor of 90 = 2*45 = 2*3*15 = 2*3*3*5

Factor of 75 = 3*25 = 3*5*5

The greatest common factors are 3 and 5

GCF = 3*5 = 15

Therefore, 15 is the largest number of groups that can be made.

b. If that many groups are formed, how many students of each grade level would be in each group?

Sixth grade = 90/15 = 6

Seventh grade = 75/15 = 5

Therefore, there would 6 sixth grade students and 5 seventh grade students in each group.

7 0

3 years ago

The heights of a random sample of 50 college students showed a mean of 174.5 centimeters and a standard deviation of 6.9 centime

Minchanka [31]

Answer:

Step-by-step explanation:

Hello!

For me, the first step to any statistics exercise is to determine what is the variable of interest and it's distribution.

In this example the variable is:

X: height of a college student. (cm)

There is no information about the variable distribution. To estimate the population mean you need a variable with at least a normal distribution since the mean is a parameter of it.

The option you have is to apply the Central Limit Theorem.

The central limit theorem states that if you have a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.

As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.

The sample size in this exercise is n=50 so we can apply the theorem and approximate the distribution of the sample mean to normal:

X[bar]~~N(μ;σ2/n)

Thanks to this approximation you can use an approximation of the standard normal to calculate the confidence interval:

98% CI

1 - α: 0.98

⇒α: 0.02

α/2: 0.01

$Z_{1-\alpha /2}= Z_{1-0.01}= Z_{0.99} =2.334$

X[bar] ± $Z_{1-\alpha /2} * \frac{S}{\sqrt{n} }$

174.5 ± $2.334* \frac{6.9}{\sqrt{50} }$

[172.22; 176.78]

With a confidence level of 98%, you'd expect that the true average height of college students will be contained in the interval [172.22; 176.78].

I hope it helps!

4 0

2 years ago

What key features are necessary and how they can be used to create the sketch of a polynomial function?

Tomtit [17]

The key features of polynomials are the vertex, axis of symmetry, x and y intercepts.

<span>1. </span>The degree will help you find the end behavior.

<span>2. </span>The vertex shows you where it changes concavity.

<span>3. </span>X and y intercepts give you a couple of points of reference.

<span>4. </span>Axis of symmetry is only applicable to even degree polynomials.

I am hoping that these answers have satisfied your queries and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.

4 0

2 years ago

HELP MY GRADE DEPENDS ON THIS!!!!

zaharov [31]

Answer:

in what number is the question ate

5 0

3 years ago

Marge cut 16 pieces of tape for mounting pictures on poster board. Each piece of tape was 3/8 inch long. How much tape did Marge

mafiozo [28]

Hi! :)

It sounds like you need to multiply this fraction.

$\frac{3}{8}$ *16=6

So, Marge used 6 total inches of tape.

Hope this helps!

5 0

3 years ago