Write the vertex form of the equation of the parabola which has a vertex of (0,0) and contains the point (1,2). A. Y=2x^2. B. Y=2(x-1)^2. C. Y=x^2. D. Y=(x+1)^2+1

Answers

Answer 1

General equation of parabola: y-k = a(x-h)^2

Here the vertex is at (0,0), so we have y-0 = a(x-0)^2, or y = ax^2

All we have to do now is to find the value of the coefficient a.

(1,2) is on the curve. Therefore, 2 = a(1)^2, or 2 = a(1), or a = 2.

The equation of this parabola is y = 2x^2.

Answer 2

The vertex form of the equation of a parabola with a vertex at (0,0) and passing through the point (1,2) is [tex]y=2x^2.[/tex]

The vertex form of a parabola is given by: [tex]y = a(x - h)^2 + k[/tex] where (h, k) is the vertex of the parabola.

In this case, the vertex is (0, 0), so h = 0 and k = 0.

Therefore, the equation becomes: [tex]y = a(x - 0)^2 + 0.[/tex] Simplifying further, the equation becomes: [tex]y = ax^2[/tex].

Now, we need to find the value of 'a.' To do this, we can use the given point (1, 2). Substitute these values into the equation:

[tex]2 = a(1)^2[/tex].

Therefore, 'a' is 2. So, the final equation in vertex form is: [tex]y = 2x^2.[/tex]

So, the correct answer is A. [tex]Y = 2x^2.[/tex]

Related Questions

A crane is rented at $1000 per day plus a charge per hour of use. The crane was used for 7 hours on a day, and the total charge was $3450. Which equation can be used to find the charge x, in dollars, per hour of use?

Answers

The equation can be (3450-1000)÷7=350.

mary draws the number line below to repersent the solution set of the inequality 50-8t<90
what mistake did Mary make?

Answers

50-8t<90
50-90<8t
-40<8t
8t>-40
t>-5
Solutions should go to the right.
Mary probably was solving it as following
50-8t<90
-8t<90-50
-8t<40 (here, when she divided both sides by -8, she had to change sign < to the sign >)
But she did not change the sign, and got
t<-5

Sudhanshu is solving a system representing a race between two remote control cars. The variable x is defined as time in seconds, and y is the distance in meters from the starting line. How many solutions should Sudhanshu find?

Answers

It all depends on the speeds of the cars. If they are going the same speed, the lines could never cross. Or they could could cross once, if one car passes the other.
However, if the speeds are changing, then there could be multiple solutions.

Answer:

The lines would only cross ONCE. So the answer is ONE.

Step-by-step explanation:

If using a graphing calculator you will see that the lines are at different slopes and will soon cross at (5,20) on a graph. Which means that the second cars is also faster even though the first car had a head start.

Find the future value of $1800 deposited at 8% for 5 years if the account pays simple interest, and the account pays interest compounded annually.

Answers

For one year:
0.08(1800) + 1800
But because it is 5 years:
5(0.08(1800)) + 1800
0.4(1800) + 1800
We can make it simpler:
1.4(1800)
Multiply:
2520
YOU NOW HAVE $2520

Answer:

The answer is 2,644.79.

You would have to calculate the three variables to get and complete your answer.

Step-by-step explanation:

Triangle BCD is similar to triangle ACE. If the triangles are isosceles, what is the length of AB?
F.) 16cm
G.) 11cm
H.) 40cm
J.) 35cm

Answers

[tex] \frac{2.75}{22} = \frac{5}{ac} \\ ac = 5 \div ( \frac{2.75}{22} ) = 40 \\ ab = 40 - 5 = 35[/tex]
Correspondind sides, similar triangles

Find the area of a parallelogram....

Answers

The area of a parallelogram is ...
A = bh
Substituting the given values, you have
A = (3x +5)(7x -1)
We presume you want the product multiplied out. Use the distributive property for that.
A = 3x(7x -1) +5(7x -1)
A = 21x² -3x +35x -5
A = 21x² +32x -5

The area of the parallelogram is 21x² +32x -5.

Can I have some help with this question?

Answers

-10(1-9x) +6(x-10)
-10+90x+6x-60

96x-70

so d is the answer

This question asks for distribution, which can be done by multiplying; then adding to the total.
-10(1-9x)=90x-10
6(x-10)=6x-60
(90x-10)+(6x-60)=96x-70 (same thing as -70+96x)
So, the answer is D. -70+96x
Have a nice day! ♪

Enter the value of 5 times (13.5-4.5)

Answers

The answer is 45 because you do parenthesis first which is 13.5-4.5=9 then you multiply 9×5=45 therefore the answer is 45.

Expansion is a means by which complex function are simplified. The value of the expression 5 times (13.5-4.5) is 45

Factorization and expansion

Expansion is a means by which complex function are simplified by multiplying the expression with one another.

Given the expression:

5(13. 5 - 4.5)

According to the distributive property:

= 5(13. 5 - 4.5)

= 5(13.5) - 5(4.5)

= 67.5 - 22.5

= 45.0

Hence the value of the expression 5 times (13.5-4.5) is 45

Learn more on expansion here: https://brainly.com/question/26430239

The big bend national park covers 800,000 acres. Brazos Bend state park covers about 5,000 acres. About how many more acres does Big Bend National Park cover then Brazos Bend state park?

Answers

795,000 I dont totally understand why you asked
this but okay....

Final answer:

Big Bend National Park is larger by approximately 795,000 acres than Brazos Bend State Park. This figure was obtained by subtracting the area of the Brazos Bend State Park from the area of the Big Bend National Park.

Explanation:

The Big Bend National Park and the Brazos Bend State Park have a substantial difference in size. You can calculate this size difference by performing a simple subtraction operation. In this case, the size of the Big Bend National Park is 800,000 acres, whereas Brazos Bend State Park covers about 5,000 acres. By subtracting the size of Brazos Bend State Park from the size of the Big Bend National Park, we will get about 795,000 acres, which represents the size difference.

So, the formula would appear as follows:
800,000 acres (Big Bend National Park) - 5,000 acres (Brazos Bend State Park) = 795,000 acres difference.

Learn more about Area Difference here:

https://brainly.com/question/28897398

#SPJ12

Add the two expressions. 4.6x−3 and −5.3x+9 Enter your answer, in simplified form, in the box. PLEASE ANSWER FAST THIS IS A BIG DEAL!!!

Answers

So you have 4.6x − 3 and −5.3x + 9. You can only add like terms, which are terms where their variables (and the exponents on the variable) are the same. That means you can add 4.6x and −5.3x, and you can also add −3 and 9:
[tex]4.6x - 3 + - 5.3x + 9\\ = (4.6x - 5.3x) + (-3 + 9)\\ = -0.7x + 6[/tex]

-----

Answer: -0.7x + 6

An expression is defined as a set of numbers, variables, and mathematical operations. The addition of the two given expressions (4.6x-3) and (-5.3x+9) is (-0.7x+6).

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The addition of the two given expressions (4.6x-3) and (-5.3x+9) is,

(4.6x-3) + (-5.3x+9)

= 4.6x - 3 - 5.3x + 9

= -0.7x + 6

Hence, The addition of the two given expressions (4.6x-3) and (-5.3x+9) is (-0.7x+6).

Learn more about Expression:

https://brainly.com/question/13947055

#SPJ2

What is the answer to part d. Thanks so much.

Answers

y=5/3x + 2 the 2 comes from where the point is on the y axis, the 5/3x comes from rise over run

y=5/3x-2. the 5/3 is the rise over run. the -2 comes from the downward shift in the graph, the previous answer is wrong.

ANSWER ASAP PLEASE!!!
Johnny wants to know how many students in his school enjoy watching science programs on TV. He poses this question to all 26 students in his science class and finds that 75% of his classmates enjoy watching science programs on TV. He claims that 75% of the school's student population would be expected to enjoy watching science programs on TV. Is Johnny making a valid inference about this population?
A. Yes, it is a valid inference because his classmates make up a random sample of the students in the school
B. Yes, it is a valid inference because he asked all 26 students in his science class
C. No, it is not a valid inference because he asked all 26 students in his science class instead of taking a sample from his math class
D. No, it is not a valid inference because his classmates do not make up a random sample of the students in the school

Answers

The answer is D. No, it is not a valid inference because his classmates do not make up a random sample of the students in the school.

Answer:D

Step-by-step explanation:

i got it right onn a test

Cheryl used 40% of her money to buy a dress and 1/5 of the remainder to buy a pair of shoes. She then donated $60 to charity and had $132 left How much money did Cheryl have at first?

Answers

Let the amount be a
Amount used for dress= 40% of a
amount left =60% of a
amount used for shoe= 1/5*60a/100=3a/25
left=60a/100-12a/100=48a/100
=>48a/100-60=132
=>a=192*100/49=400
She had $400 at first.
Hope I helped, good luck.

Let the amount of money she has at first be x.

Dress = 40% x = 0.4x

Amount left = x - 0.4x = 0.6x

Shoes = 1/5 x 0.6x = 0.12x

Amount left = 0.6x - 0.12x = 0.48x

Donated $60 and had $132 left:
⇒ 0.48x - 60 = 132

Solve x:

0.48x - 60 = 132

0.48x = 192

x = $400

Answer: $400

Solve the equation (x-5)1/2+5=2

Answers

The first thing we are going to do for this case is to rewrite the equation correctly:
((x-5) ^ (1/2)) + 5 = 2
Clearing x we have:
(x-5) ^ (1/2) = 2-5
(x-5) ^ (1/2) = -3
x-5 = root (-3)
x-5 = i * root (3)
x = 5 + i * root (3)
Answer:
The value of x is given by:
x = 5 + i * root (3)

(x - 5)1/2 + 5 = 2
(x - 5)1/2 + 5 - 5 = 2 - 5
(x - 5)1/2 = -3
1/2x - 2.5 = -3
1/2x - 2.5 + 2.5 = -3 + 2.5
1/2x = -1/2
(1/2x)/(1/2) = (-1/2)/(1/2)
x = -1 <-------------answer :)

Find f(x) if it is known that f(3k)=3k+7.

Answers

f(3k)=3k +7 Equals 9k+7. So 9k+7 would be the Answer.

Since f(3k) = 3k+7 (Equation 1)

We have to determine the value of f(x).

That is we have to replace 3k by x,

3k = x

Substituting the value of 3k in equation 1.

So, f(x) = x + 7

Therefore, f(x)=x+7 is the required function.

Please help me answer this question. Explain if possible.

Answers

The functions have the same initial value is correct

"The functions have the same rate of change" is wrong because as we can see, the table goes up by 10, however, the graph goes up by 15

"Both functions are the same" is also wrong, we already proved they have a different slope, how could they possibly be the same?

"The rate of change for Tour 1 is greater" is also wrong because tour 2 goes by 15, which is greater than 10.

"The functions have the same initial value is correct because as we can see on the graph(tour 2), the y-intercept is 35, using the slope on the tab;e(tour 1) we can calculate that when x is 0, the y-value is 35, which means both of the tours has a y-intercept of 35, therefore, this is the correct choice

It's possibly "The functions have the same rate of change."

Explanation: Alright let's do answer of elimination. It cannot be "Both functions are the same" Due to the fact that for one person in Tour 1 is 45 dollars while for Tour 2 is 50. It cannot be "The functions have the same initial value. Since for initial value it's kind of like a constant. For example for 1 person it would be 20 dollars for 2 it would be 40 and so on. It cannot be the last one since rate of change is obviously different. I don't think I have to go into that.

Also I see your doing an IReady Lesson

Originally priced at $15.99 was marked down 15% and then it was moved to a clearance rack marked take an additional 50% off the lowest marked price what is the final price of the PlayStation game

Answers

First, the mark down 15% would make the value 85% of the original, so doing 15.99*0.85 gives you 13.59. Then take that and multiply that by 0.5, because of the half price, to get a final price of $6.79

What is the formula for the perimeter of a rectangle?

Answers

A= L x W / 2 length times width divided by 2

What is the range of the following graph?

Answers

Range is the set of possible y values. If you look at the end behavior of the function, as x approaches both infinity and negative infinity, y continues to increase in magnitude, meaning that the range is from negative infinity to infinity. the correct answer is B.

what does a highter and lower standard deviation tell you!!!!?
what does a higher and lower z-score tell you ?
what does the varience tell you?

Answers

The larger the standard deviation, the more spread out the data values will be. A smaller standard deviation, and the values are more closely grouped together. The variance is equal to the standard deviation squared. In terms of symbols
V = s^2
where V = variance and s = standard deviation
So the variance can also be used to determine how grouped or spread out the data values are

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

The z score tells us where this score is located in terms of the group. If the z score is positive, then it is above the mean. If the z score is negative, then it is below the mean. The further the z score is from zero, the further the raw score is from the mean. A score of z = 0 is right at the mean.

A patrolman spends 25% every day completing paperwork. The patrolman’s shift each day is 8 hours. How much of his time does he spend doing paperwork each day?

Answers

[tex]8 \times 25\% \\ = 8 \times \dfrac{25}{100} \\ = 2[/tex]

Answer : He spends 2 hours doing paperwork each day.

Hope this helps. - M

The equation below shows The area of a trapezoid, a, with a height of 9 cm, and one base 35 cm. A=9/2(b+35)
Which formula correctly solves for the other base, b?

Answers

For this case we have the following equation:
A = 9/2 (b + 35)
We must clear b from the equation, to obtain the value of the other base.
Clearing b we have:
(b + 35) = (2/9) A
b = (2/9) A - 35
Answer:
A formula that correctly solves for the other base, b is:
b = (2/9) A - 35

Kristen invests $5,745 in a bank. The bank pays 6.5% interest compounded monthly. How long must she leave the money in the bank for it to double? Round to nearest tenth of a year.

Answers

To solve this we are going to use the compounded interest formula: [tex]A=P(1+ \frac{r}{n})^{nt} [/tex]
where
[tex]A[/tex] is the final amount
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is the time in years

We know that initial investment is $5,745, so [tex]P=5745[/tex]. We also know that Kristen wants his investment to double, so [tex]A=2*5745=11490[/tex]. Now, to convert the interest rate to decimal form, we are going to divide the rate by 100%: [tex]r= \frac{6.5}{100}=0.065 [/tex]. Since the interest is compounded monthly, it is compounded 12 times per year: therefore, [tex]n=12[/tex]. Now that we have all the information we need, lets replace the values in our formula and solve for [tex]t[/tex]:
[tex]A=P(1+ \frac{r}{n})^{nt} [/tex]
[tex]11490=5745(1+ \frac{0.065}{12})^{12t} [/tex]
[tex] \frac{11490}{5745} =(1+ \frac{0.065}{12})^{12t}[/tex]
[tex]2=( \frac{2413}{2400} )^{12t}[/tex]
[tex]ln(2)=ln(\frac{2413}{2400} )^{12t}[/tex]
[tex]ln(2)=12tln(\frac{2413}{2400} )[/tex]
[tex] \frac{ln(2)}{12ln(\frac{2413}{2400} )} =t[/tex]
[tex]t=\frac{ln(2)}{12ln(\frac{2413}{2400} )}[/tex]
[tex]t=10.7[/tex]

We can conclude that she must leave the money for 10.7 years in the bank for it to double.

Robin’s scores: 99, 108, 102, 107, 119 Evelyn’s scores: 125, 137, 138, 145, 145 Find and compare the medians of the data sets. Do the medians support your conclusion that Robin is winning the game?

Answers

To find the median, just sort the numbers from least to greatest and find the number in the center.

Robin's scores: 99, 102, 107, 108, 119. Median is 107.

Evelyn's scores: 125, 137, 138, 145, 145. Median is 138.

The median from Evelyn's scores is greater than the median from Robin's. Therefore, the medians do NOT support the conclusion that Robin is winning the game.

Answer:

The median score for Robin is 107. The Median Score of Evelyn is 138. The medians are the same as the means, so the same conclusion that Robin is winning will be drawn.

Step-by-step explanation:

Find the area of the trapezoid to the nearest tenth.

Answers

The area of the trapezoid would be 153. What I’d did was 1.3 added to 1.5 added to 0.6, multiplied by 45, and I got the answer of 153.

what does x equal
5x+2y=3
1x+2y=6

Answers

[tex]\underline{-\left\{\begin{array}{ccc}5x+2y=3\\x+2y=6\end{array}\right }\ \ \ \ |subtract\ both\ sides\\\\4x=-3\ \ \ |:4\\\\x=-\dfrac{3}{4}\to x=-0.75[/tex]

A researcher randomly surveyed a sample of high school students in a town to find out which career area they were most interested in pursuing. This table shows the results of the sample. The town has a total of 1000 high school students.

Art Science Finance Health Law Education
26 24 16 21 18 20
Based on this sample, how many high school students in the school are predicted to be most interested in pursuing a career in health?

Enter your answer in the box.

Answers

total of students sampled:
26 + 24 + 16 + 21 + 18 + 20 = 125 total
21 picked health so 21 / 125 = 0.168 of the students picked health
multiply that by total students:
1000 * 0.168 = 168 total students will pick health

The total number of students who will pick health is 168 if a researcher randomly surveyed a sample of high school students in a town.

What is a survey?

A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.

We have:

A researcher randomly surveyed a sample of high school students in a town to find out which career area they were most interested in pursuing.

The town has a total of 1000 high school students.

Total of students sampled = 26 + 24 + 16 + 21 + 18 + 20

= 125 total

21 picked health:

= 21 / 125

= 0.168 of the students picked health

Total students will pick health:

= 1000×0.168

= 168

Thus, the total number of students will pick health is 168 if a researcher randomly surveyed a sample of high school students in a town.

Learn more about the survey here:

brainly.com/question/17373064

#SPJ2

370x1/10 = please help

Answers

37,
It is thirty seven, use a calculator

Answer: 37
This is because 370 times 1/10 is the same as 370 times 0.1 which would be equal to 37

vector works the same number of hours every week he worked a total of 532.5 and hours in the last 15 weeks. how many hrs did he work in one week

Answers

532.5/15
this will give you the hours in one week
= 35.5

Divide 532.5 hours by 15 weeks.
532.5/15 = 35.5

Vector worked 35.5 hours in one week.

Can someone please help me with number 25

Answers

Answer:

x² + 10x + 24 = (x + 4)(x + 6)

b = 4 or 6

Other Questions

These statements are important to historical essays because they:A. Signal that an article will be argued rather than explanatory B. Prepare readers for the evidence presented in an essay C. Ensure that nobody can make counterclaims against an essay D. Allow the author to paraphrase sources rather than quoting them. Which of the following was founded primarily to promote nationalist goals?A. OPECB. Nonaligned MovementC. the Congress PartyD The United Nations10. What is one similarity between Nigeria and Pakistan>A Bothe countries won indpendece primarilly through armed struggleB in both countries, ethnic groups tried to break away and form separate nationsc both countries benefited from the discovery of oil deposits d both countries gained independence from britain in the 1940's11. The genocide in Rwanda resulted from a long conflict betweena christians and muslimsb an ethnic majority and minorityc supporters of the soviet uniton and the usd white colonists and the black majority12which name belongs in the empty cell. India - _____a muhammad ali Jinnahb jawaharlala Nehruc suhartod ferdinand marcos13 What is one ongoing obstacle to peace between Israel and Palestinian Arabsa israel will not give up its settlements on the sinai b palestinian refugees want to return to the land they lefr in israelc the plo continues to deny israel's right to existd Jordan and syria have refused to negotiate with israel14 what ongoing issue in teh middle east does this passage illustratea the failure of pan arabismb the rise of radical islamic fundamentalismc the struge of ethnic minoriteis for rights d the fight agains authoritarian governments15 these women and children from darfur are refugees from a conflict betweena muslims and non muslimsb arabs and non arabsc tutis and hutusd algerians and the french16 which of the following nations has largely managed to avoid serious conflict resulting from ethnic or religious diversitya malaysiab indonesiac iraq nigeria17 how did Rhodesia differ from all other african nations that declared indpendence in the 1960sa it achieved independece through peaceful meansb it was able to build a stable democratic gvtc it quickly became engulfed in civil ward it declared independence in order to preserve white minority rule 20 what is one similarity between algeria and nigeriaa both were british colonies vefore winning independenceb bothe were achieved independece largely through peaceful meansc both were able to set up stable democratic govtd both faced periouds of religious conflict and violence21 which ethnic group was successful in their attempt to separate from another country and fortm their own nationa the ibob bengalisc the kurdisd tamils22 at the time this speech was given what was the most serious of the "clouds referred to by nehrua british rule over indiab conflict caused by partition c the assassination of gahndid sikh separatism23 what event caused turmoil in this regioun during th time perioud indicated on the mapa war broke out between iran and iraqb saudi arabia led an oil embaro against usc iraq invaded kuwaitd iran experienced an islamic revolution24 what movement is described in the passage abovea the arab springb the intifadac iran's islamic revolutiond the end of the mandate system25 the struggles for independence in both angola and zaire were strongly influenced by the a discover of oilb fight against apartheidc cold ward rise of islamist partiesSORRY FOR THE SPELLING MISTAKES ITS A NEW COMPUTER p(x)= x^3+4x^2-8x-6 a= -2 how did chinese communism differ from soviet communism Equus caballus is the scientific name for a domestic horse. Equus zebra is the scientific name for a zebra. Which of the following statements is true?1. The domestic horse belongs to the Equus order.2. The domestic horse belongs to the caballus genus.3. The zebra and domestic horse belong to the same species.4. The zebra and domestic horse belong to the same genus. Studies conducted by adler et al. (1994), kelley et al. (2005) and the institute of medicine (iom) have concluded that an individual's health outcomes will be affected, in part, by in a solution of seawater water is the solute true or false?? A proton and an electron are held in place on the x axis. The proton is at x = -d, while the electron is at x = +d. They are released simultaneously, and the only force that affects their motions is the electrostatic force of attraction that applies to the other. Which particle reaches the origin first? Give your reasoning. How were western lands to be dealt with under the articles? Deon worked 16 hours last week at the grocery store and earned $124.00. If he continues to earn the same hourly pay, how many additional hours must he work to earn another $186.00? A.20 hours B.24 hours C.32 hours D.62 hours evaluate ab for a = 2 3/4 and b = 4/5 Which of the following was a major weakness of the Articles of Confederation?Select one:A. The government signed a treaty of alliance with France in 1778B. The government negotiated an end to the American RevolutionC. The government gave citizens of all states the same rightsD. The national government lacked the ability to tax A rectangle is 12 feet long and 5 feet wide. If the length of the rectangle is increased by 25% and the width is decreased by 20%, what is the change in the area of the rectangle? Which information is provided explicitly in this passage?A)Hiawatha was a gifted and talented public speaker.B)The Iroquois people united in order to protect their crops.C)The Iroquois Confederacy is comprised of five different tribes.D)Schools are named in honor of Hiawatha, primarily in the Midwest. realtor makes 3% commission. What is the commission on a $200,000 house? The motivating potential score (mps) is calculated as part of using _____. Tony collected data on years of employment and the annual salaries of the sales people at Company Z. He made a scatter plot and drew a trend line that approximated the line of best fit for the data, as shown on the right. Based on the trend line drawn for the data, what is the salary a salesperson with 3 years of employment at Company Z can expect to earn? What disease of the nervous system is also referred to as water on the brain? Find the coordinates of the third vertex that completes the construction of a right triangle on the coordinate plane.Help Me Please!!!! Which president would be most closely associated with the concept of manifest destiny?