What is the quadratic function with the given vertex and through the given point? Write the equation of the parabola in vertex form and describe how the function was transformed from the parent function y = x2.
vertex (0, 0), point (−2, 2)

Answers

Answer 1

1) The vertex equation of the quadratic function has the form:

y = A(x - h)² + k

Where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.

The coefficient A may be found when you have another point of the quadratic function.

2) Therefore, being the vertex (0,0), h = 0 and k = 0, and the equation is

y = Ax²

3) Replacing the coordinates of the point (-2,2) into the equation you get:

2 = A (-2)² ⇒ A = 2/4 = 1/2

4) The resulting equation is y = (1/2)x² ← answer

Since, the system is giving me an error, I had to put the second part of the answer in a separate file. Please, see the attached pdf file.

Answer 2

Final answer:

The quadratic function with vertex (0, 0) and passing through the point (-2, 2) is y = 0.5x^2. This is a transformation of the parent quadratic function y = x^2 with a vertical stretch by a factor of 0.5.

Explanation:

The quadratic function with the given vertex (0, 0) and going through the point (-2, 2) can be written in the form of the vertex form of a quadratic function i.e. y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Since the vertex given is (0,0), the function becomes y = ax².

Now, to find the value of 'a', we can substitute the x and y coordinates of the given point (-2,2) into the equation. So, 2 = a(-2)², this simplifies to 2 = 4a. Solving for 'a', we get a = 0.5. So, the function is y = 0.5x².

This function is a transformation of the parent function y=x². The 0.5 in front of x² means that the graph of the function stretches vertically by a factor of 0.5. Thus, the parabola opens upwards and is narrower than the parent function.

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Related Questions

at the market,8 apples cost $4.How much do 9 apples cost?

Answers

Divide the price by amount to find out how much each costs. multiply that by 9. 4 (divided by) 8 = .5, or 50cents. each apple is 50cents. multiply .50 by 9. It costs 4.50. Hope this helps

Hello!

If you divide 8 by 4, it seem that 2 apple costs $1.00. It also seems that whenever there is an odd number of apples, the cost of those apples have a cent count of 0.50 cents. So if 8 apples are $4.00, then I believe that 9 apples are $4.50.

I hope this helps!

The sum of two numbers is 43 . The larger number is 11 more than the smaller number. What are the numbers

Answers

a- one number
b- second number

a + b = 43 (the sum of two numbers is 43)
(a +11) = b (he larger number is 11 more than the smaller number)

so:
a + b = 43
a + (a + 11) = 43
a + a + 11 = 43
2a = 43 - 11
2a = 32
a = 16

now:
a + b = 43
16 + b = 43
b = 43 - 16
b = 27

that is:
a = 16
b = 27

--------------------------

checking:

b - a = 11
27 - 16 = 11 (TRUE)

Factor x3 + 2x2 + x completely

Answers

Answer:

x(x+1)²

Step-by-step explanation:

x is a common factor to all terms so the first step is to factor it out:

... x(x² +2x +1)

The quadratic factor is recognizable as the square (x+1)², so the factoring is ...

... x(x +1)²

Answer:

Step-by-step explanation:x(x+1)2

Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all of the headphones and music players in identical packages.
What is the greatest number of packages Tim can make?

Answers

Tim can put 1 music player and 3 pairs of headphones in each of 13 packages.

The greatest number of identical packages Tim can make is 13.

If you roll a fair six-sided die and a fair four-sided die, what is the probability that neither die shows a 1?

Answers

Answer in fraction form: 5/8
Answer in decimal form: 0.625

==============================================

Explanation:

There are 5 sides that aren't labeled "1" out of 6 total. So the probability of not rolling a "1" on the six-sided die is 5/6

Similarly, there are 3 sides that aren't labeled "1" out of 4 sides on the four-sided die. The probability of not rolling a "1" for this die is 3/4

Multiply the fractions
(5/6)*(3/4) = (5*3)/(6*4) = 15/24 = 5/8

The answer in fraction form is 5/8 which converts to 0.625 (use long division or a calculator)

Note: the multiplication of probabilities works because the two events (of rolling each die) are independent

hey can some one help me with this

Answers

Hello!

First you have to find the surface area of what he is painting

Finding the areas of all the rectangles he is painting

14 * 8 = 112
14 * 8 = 112
12 * 8 = 96
12 * 8 = 96
12 * 14 = 168

Add all these up

112 + 112 + 96 + 96 + 168 = 584

Divide this by the amount of area a pint of paint covers

584 / 90 = 6.4888...

He needs 7 pints of paint because he needs more than 6

Multiply this by the cost of 1 pint of pint

7 * 7.98 = 55.86

The answer is $55.86

Hope this helps!

The area of a rectangular surface is given by the product of its length and width. The total area Jake wants to paint is that of the four side walls and the ceiling. That is ...
A = (8 ft)(14 ft) +(8 ft)(12 ft) +(8 ft)(14 ft) +(8 ft)(12 ft) +(14 ft)(12 ft)
A = (8 ft)*2*(14 ft +12 ft) +(14 ft)(12 ft) . . . . rearranging to simplify a bit
A = 2*(8 ft)(26 ft) +(14 ft)(12 ft)
A = 416 ft² +168 ft²
A = 584 ft²

6 pints of paint will cover 6*(90 ft²) = 540 ft², not quite enough. The next higher multiple of 90 ft² is 7*(90 ft²) = 630 ft², more than adequate.

Jake will need to purchase 7 pints of paint.

The cost of Jake's purchase will be 7*$7.98 = $55.86.

identify the two rational numbers. A) √2 B) 1.01 C) 1.010010001... C) -2/5

Answers

Rational numbers can be written as fractions. A is an irrational number because it has infinite digits that cannot be written as a fraction. B is a rational number because it has finite digits. C is an irrational number because it has infinite digits that cannot be written as a fraction. D is rational because it is a fraction.

So -2/5 and 1.01 are rational.

We have that for the Question "identify the two rational numbers. " it can be said that

Option B,C,D is rational

From the question we are told

identify the two rational numbers.

A)√2

B) 1.01

C) 1.010010001...

D) -2/5

Generally

Rational number are real number that exist is a form where the denominators are not zero

Therefore

A)√2 this is an irratioanl number as its \pm 1

B) 1.01 Rational

C) 1.010010001... rational

D) -2/5 rational

Hence

Option B,C,D is rational

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Let f(x) = -6x + 3 and g(x) = 5x + 4. Find f*g and state its domain.

-18x2 - 39x + 20; all real numbers except x = 1

-30x2 - 9x + 12; all real numbers

-18x2 - 39x + 20; all real numbers

-30x2 - 9x + 12; all real numbers except x = 4

Answers

1- getting f*g:
We are given that:
f (x) = -6x + 3
g (x) = 5x + 4
To get f*g, we will simply multiply the two functions as follows:
f (x) * g (x) = (-6x+3)(5x+4)
f (x) * g (x) = -30x² - 24x + 15x + 12
f (x) * g (x) = -30x² - 9x + 12

2- getting the domain:
The domain is all the values of x that can be used in the given equation.
In the equation calculated from part 1, we can note that all real numbers can be considered as the domain.

Hope this helps :)

-1+7n
A. Quadratic monomial
B. Quadratic trinomial
C. Linear binomial
D. fifth degree binomial
E. none

Answers

-1+7n
A. Quadratic monomial
B. Quadratic trinomial
C. Linear binomial
D. fifth degree binomial
E. none

The correct answer is:

C. Linear binomial

Linear binomial is a polynomial of the first degree: ax+ b. If to divide a polynomial, containing a letter x, by a linear binomial x – b, where b is a number ( positive or negative ), then a remainder will be a polynomial only of zero degree, i.e. some number N , which can be found without finding a quotient.

Four pencils are held together with a band.
the figure on the right shows the bottom end of the pencils and the band.
each of the pencils has a diameter of 10mm
find the length of the band in this position.
give your answer in terms of pi.

Answers

Answer: (40+10π) mm.

Step-by-step explanation: Given diameter of the circle = 10mm.

Radius of the circle = 10/2 = 5 mm.

From the figure, we can see that each or the four corners makes a quarter of the circle.

And four corners would make the complete circle with radius 5mm.

Therefore, circumference of the four quarters of a circle = 2 π r

= 2 π (5) = 10 π.

Now, we can see that each side 10 mm of band also there.

So, the length of straight band on all four sides = 4 × 10 = 40 mm.

Total length of the band = (40+10π) mm

The length of the band is the number of units it covers

The actual length of the band is: [tex]\mathbf{40 + 10\pi}[/tex]

The diameter of 1 pencil is given as:

[tex]\mathbf{d = 10}[/tex]

The circumference of 1 pencil is:

[tex]\mathbf{C = \pi d}[/tex]

So, we have:

[tex]\mathbf{C = 10\pi }[/tex]

Multiply by 4, to calculate the circumference of all pencils

[tex]\mathbf{4C =4 \times 10\pi }[/tex]

[tex]\mathbf{4C =40\pi }[/tex]

The rubber band covers a quarter of the 4 pencils.

So, we divide by 4

[tex]\mathbf{C = 10\pi }[/tex]

The length of the band on one pencil is:

[tex]\mathbf{L = 10}[/tex]

Multiply by 4, for the 4 pencils

[tex]\mathbf{L = 40}[/tex]

So, the actual length of the band is:

[tex]\mathbf{Length = 40 + 10\pi}[/tex]

Answers

Hey there!

The median is the number in the middle when the numbers go from least to greatest. This would be 4, 5, 8, 9, 10. The middle number would be 8. A way to find the middle number is to mark off the end number on the right and left side until you are left with 1 number. If you are left with 2, add the numbers up and divide. The answer to this is 8.

I hope this helps!

Hello There!

Median: The middle number when all the numbers are listed in oder from least to greatest.

To find the median, place the numbers in order from least to greatest.

In this case, the numbers would be 4, 5, 8, 9, 10

The middle number would be 8 so the median for this set of numbers is 8.

write percent as a fraction or in simplest form of 37.5%

Answers

37.5% is equivalent to a fractional form. You get this by putting 37.5 over 100 since per cent means per one-hundred. This gives us
37.5% = 37.5/100 = 375/1000 = 3/8
The simplest form is 3/8, therefore the answer to your question is 3/8.

The answer is 3/8 because 3 ÷ 8 = 0.375

0.375 = 37.5%

Answer = 3/8

~Hope this helped~

Minimze the product of a positive rational number and a negative rational number, given that the positive number is exactly 8 greater than the negative number. what is the final product?

Answers

If we let x represent the negative rational number, then the product is
x(x+8)
This describes an upward-opening parabola whose vertex is (-4, -16).

The numbers are -4 and +4, and the final product is -16.

Simplify.
600(1+0.03)^12

Answers

The answer is 855.45653210

The above answer will be calculated as -

We are given -

600 ( 1 + 0.03)^12

We will first add - 1 + 0.03 = 1.03

Now, we will multiply 1.03 into 12 times, in order to find the value of ( 1.03)^12

The answer for ( 1.03)^12 = 1.4268

Now, we will multiply 1.4268 with 600

600 × 1.4268 = 856.08 approximately.

Thus, the value of 600*(1.03)^12 has been calculated.

If 2 fluid ounces equals 60 milliliters , how many milliliters are in 7 ounces of cough syrup

Answers

210 fluid ounces is your answer, hope this helps!!!

find (f o g)(2) and (f+g)(2) when f(x)=1/x and g(x)=4x+9

Answers

I believe the answers are:
(f o g) (2)= 1/17 and (f+g) (2)= 17.5

Final answer:

To find (f o g)(2), substitute the value of g(2) into f. To find (f+g)(2), find f(2) and g(2) separately, then add them together.

Explanation:

To find (f o g)(2), we need to first find g(2), and then substitute that value into f. To find g(2), we substitute 2 into the expression for g(x). g(2) = 4(2) + 9 = 8 + 9 = 17. Now, we substitute 17 into the expression for f(x), which is 1/x. (f o g)(2) = f(g(2)) = f(17) = 1/17.

To find (f+g)(2), we first need to find f(2) and g(2) separately. f(2) = 1/2, and g(2) = 17. Now, we add them together. (f+g)(2) = f(2) + g(2) = 1/2 + 17 = 1/2 + 34/2 = 35/2 = 17.5.

2 + 3 × 16 − 2 × 21 − 3

Answers

By the order of operations, the answer is 5.

The order of operations is PEMDAS -
· Parenthesis
· Exponents
· Multiplication
· Division
· Addition
· Subtraction

Thus, we would multiply 3 with 16 and 2 with 21 first.

2 + 3 × 16 - 2 × 21 - 3
2 + 48 - 42 - 3

Now we combine the terms from left to right.

2 + 48 - 42 - 3
50 - 42 - 3
8 - 3
5

Answer:
5

Final answer:

To solve the expression 2 + 3 × 16 − 2 × 21 − 3, we use the order of operations rule, starting with multiplication to get 48 and 42, followed by addition and subtraction to arrive at the final answer of 5.

Explanation:

The student's question requires us to solve a mathematical expression using the correct order of operations. In the expression 2 + 3 × 16 − 2 × 21 − 3, we need to follow the BIDMAS/BODMAS/PEMDAS rule (Brackets, Indices/Orders, Division and Multiplication, Addition and Subtraction). This rule ensures that we perform multiplication and division before addition and subtraction.

First, we calculate the multiplication parts: 3 × 16 and 2 × 21.
3 × 16 = 48
2 × 21 = 42

Substituting these into the original expression gives us:
2 + 48 − 42 − 3

Next, we perform the addition and subtraction in order from left to right:
2 + 48 = 50
50 − 42 = 8
8 − 3 = 5

So, the expression simplifies to the number 5.

Hey can you please help me posted picture of question

Answers

To find the number of possibilities, we multiply the number of things together:
7*2*4*4
14*4*4
64*4
244
There are 244 combinations

Q # 4 Solve the graph please <6. , <1. , <2. ,<4

Answers

The interior angel of 7 will be angel 4
∠7 + ∠4 = 180°

You help build a new play center at a daycare. The play center has a tunnel for the children to climb through. You are painting the outside of the tunnel. Find the approximate surface area of the outside of the tunnel so you know how much area you need to paint. Use 3.14 to approximate pi.

Answers

To answer your question, I need to know the radius or diameter and the height of the object

(n+8)+(n−12) =
what is the answer

Answers

The simplification of ( n + 8) + ( n -12 ) is 2(n -2)

algebraic expression are expression with unknown.

This unknown is represented by letters and in linear algebraic equations , the highest power of the unknown is 1.

Simplifying (n + 8) + (n-12)

n + 8 + n -12

collecting like terms

n + n + 8 -12

2n -4

we can further Factorize

2( n -2)

Therefore, the simplification of ( n + 8) + ( n -12 ) is 2(n -2)

What is the measure of ∠N?

Answers

the sum of all interior angles in a polygon is

180( n - 2 ), n = number of sides in the polygon.

this one is a QUADrilateral, so it has 4 sides, thus its interior angles add up to 180( 4 - 2), or 360°.

thus 75 + 104 + 59 + ∡N = 360, ∡N = 360 - 75 - 104 - 59.

Simplify
cosx ( tanx+cotx)

Answers

The first step to solving this is to use tan(t) = [tex] \frac{sin(t)}{cos(t)} [/tex] to transform this expression.
cos(x) × [tex]( \frac{sin(x)}{cos(x)} + cot(x) )[/tex]
Using cot(t) = [tex] \frac{cos(x)}{sin(x)} [/tex],, transform the expression again.
cos(x) × [tex]( \frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)} )[/tex]
Next you need to write all numerators above the least common denominator (cos(x)sin(x)).
cos(x) × [tex] \frac{sin(x)^{2} + cos(x)^{2} }{cos(x)sin(x)} [/tex]
Using sin(t)² + cos(t)² = 1,, simplify the expression.
cos(x) × [tex] \frac{1}{cos(x)sin(x)} [/tex]
Reduce the expression with cos(x).
[tex] \frac{1}{sin(x)} [/tex]
Lastly,, use [tex] \frac{1}{sin(t)} [/tex] = csc(t) to transform the expression and find your final answer.
csc(x)
This means that the final answer to this expression is csc(x).
Let me know if you have any further questions.
:)

Final answer:

The expression cosx (tanx+cotx) simplifies to sinx+cosx by using trigonometric identities and recognizing that tanx and cotx can be expressed in terms of sinx and cosx, allowing terms to cancel out.

Explanation:

To simplify the expression cosx (tanx+cotx), we need to use trigonometric identities. Recall that tanx = sinx/cosx, and cotx = cosx/sinx. Therefore, when we multiply cosx by tanx, the cosx in the numerator and denominator will cancel out, leaving us with sinx. Similarly, when we multiply cosx by cotx, sinx in the numerator and denominator will cancel out, leaving us with cosx.

So the simplification process will look like this:

cosx * tanx = sinx

cosx * cotx = cosx

Thus, cosx (tanx+cotx) = sinx+cosx.

This is the simplified form of the expression given. It's important to remember that trigonometric identities are a powerful tool in simplifying expressions involving trigonometric functions.

45 points!!!❤
Northwoods Middle School chorus 3/8 of the members are 11 year olds of the 11 year old chorus members 2/5 are boys what fraction of all the chorus members are 11 year old boys

Answers

3/20

Simply do 3/8 times 2/5 to find this

3/8 of he chorus are 11 year olds.

2/5 of the 11 year olds are boys.

so 2/5 of 3/8 are 11 year old boys.

2/5 * 3/8 = 3/20 is da answer.

√x<4 A.20 B.12 C.2 D.-1 E.5. F. No solution

Answers

We know that for √x to be meaningful, we must have x ≥ 0.

If we square both sides of the inequality, we have
x < 4²
x < 16

Thus the whole solution is
0 ≤ x < 16

The following choices are valid solutions to the inequality:
B. 12
C. 2
E. 5

Dave krug finances a new automobile by paying $6,500 cash and agreeing to make 40 monthly payments of $500 each, the first payment to be made one month after the purchase. the loan bears interest at an annual rate of 12%. what is the cost of the automobile?

Answers

P = (C - down payment)*D

D = [i/12]/[1-(1+i/12)^-12n] = [0.12/12]/[1-(1+0.12/12)^-40] = 0.03046

Therefore,

500 = (C-6,500)*0.03046
C-6,500 = 500/0.03046 = 16,417.34
C = 22,917.34

The cost of the automobile was $22,917.34

Final answer:

The cost of the automobile, excluding the impact of the interest, is $26,500.

Explanation:

For this question, we need to determine the total cost of the automobile purchased by Dave Krug. We know that Dave made an upfront payment of $6,500, and also agreed to make 40 monthly payments of $500 each. The total amount paid through monthly payments is $500 * 40 = $20,000.

Here, it is also stated that the loan bears an annual interest rate of 12%. However, no additional data are given for us to calculate the impact of the interest on the overall cost of the car. So, we'll proceed without including the interest.

So, to find the total cost of the car, we combine the upfront payment with the total monthly payments. That is, $6,500 (upfront payment) + $20,000 (total monthly payments) = $26,500. Therefore, the cost of the automobile without taking into account the interest is $26,500.

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Final answer:

For every mole of carbon dioxide used, one mole of methane is produced. Therefore, 71.1 moles of carbon dioxide would produce 71.1 moles of methane, assuming hydrogen is in excess.

Explanation:

According to the given reaction, we can infer that the stoichiometric ratio between methane (CH4) and carbon dioxide (CO2) is 1:1. This means for each mole of methane produced, one mole of carbon dioxide is consumed. Therefore, if you are starting with 71.1 moles of carbon dioxide and assuming there is excess hydrogen, you would produce 71.1 moles of methane because of this 1:1 mole ratio.

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Your salary is $25,000 you just received a 2.5% pay increase for the year. What is your new salary?

Answers

Hey there!

Here is your answer:

The proper answer to this question is "$25,625".

Reason:

In order to add a 2.5% increase on a pay check you have to multiply 25,000 by 1.025.....

25,000×1.025=$25,625

Therefore my new salary is $25,625!

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

To win at lotto in one state, one must correctly select 5 numbers from a collection of 58 numbers (1 through 58). the order in which the selection is made does not matter. how many different selections are possible?

Answers

Asked and answered elsewhere.
https://brainly.com/question/9998342

Equation 1: m = 6 + n Equation 2: 2m = 8 + 8n Step 1: −2(m) = −2(6 + n) 2m = 8 + 8n Step 2: −2m = −12 − 2n 2m = 8 + 8n Step 3: −12 − 2n = 8 + 8n Step 4: −20 = 10n Step 5: n = −2 In which step did the student first make an error? (4 points) Step 2 Step 3 Step 4 Step 5 4 points Click Save and Submit to save and subm

Answers

Answer:

step three is the incorrect one making step three the answer

Step-by-step explanation:

In the following steps student made the error in the third step.

What is an Equation ?

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

The error occurred in Step 3.

Step 3 should be:

-2(m) = -2(6 + n)

-2m = -12 - 2n

The mistake was that the student distributed the negative sign only to the 6 and not to the n.

The correct next step is to simplify equation 2:

2m = 8 + 8n

So the student made an error in Step 3.

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hey can you please help me posted picture of question

Answers

Considering the function: G(x)= 4-x^4

Graph using selected points:
\Falls to the left and falls to the right:

x y
-2 -12
-1 3
0 4
1 3
2 -12

Then plot the points given:
See attached picture:

As observed in the provided picture, the graph shows that the function G(x)= 4-x^4 has the same graph in the given problem.

If you observe the two graphs, the graph of G(x) is shifted vertically up by 1 unit as compared to F(x).

So the relation between two graphs can be written as:

G(x) = F(x) + 1

Using the value of F(x), we get:

G(x) = 3 - x⁴ + 1

So,

G(x) = 4 - x⁴

Thus, option A gives the correct answer.

Other Questions

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What is the quadratic function with the given vertex and through the given point? Write the equation of the parabola in vertex form and describe how the function was transformed from the parent function y = x2. vertex (0, 0), point (−2, 2)

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What is the quadratic function with the given vertex and through the given point? Write the equation of the parabola in vertex form and describe how the function was transformed from the parent function y = x2.
vertex (0, 0), point (−2, 2)