A parabola having its axis vertical passes through three points A(0,0), B(1,0), and C(5,-20) respectively. Determine the coordinates of the vertex of the parabola.

Answers

Answer 1

Answer:

(1/2, 1/4)

Step-by-step explanation:

This is gonna be long. The x coordinate of a parabola's vertex = -b/2a. Now we have to find the equation of the parabola. Using the given points and plugging them into y=ax^2 + bx + c, we can determine:

0 = c

0 = a + b

-20 = 25a + 5b

After rearranging and solving, we get:

b = -a

-20 = 20a

a = -1

b = 1

y = -x^2 + x

Now we can find the x coordinate of the vertex, which is 1/2. After plugging this into our parabola, we get a y coordinate of -1/4 + 1/2 = 1/4. Therefore, the vertex is located at (1/2, 1/4).


Related Questions

Please help and explain if you can the answer because I don’t know what I’m doing

Answers

Answer:

Step-by-step explanation:

Pls help asap the best I can do is 50 points
Answer the ones where the zeros are those are the one that I did bad or left blank

Answers

Step-by-step explanation:

8.a.

a function is something that looks like

y = ax + b or similar.

it describes the way to calculate the result for whatever input value you can come up with.

so,

C = 12×d + 8

you could also say

C(d) = 12×d + 8

as, when you rent, you have to pay these $8 in any case, no matter how long you stay, and you need to pay $12 per day you stay.

funny thing is : you understood this perfectly well when doing b.

c.

the constant rate of change is always the factor of the input variable. here : 12

it is the ratio of (y change) / (x change)

or here (C change / d change).

it indicates that for any increase of d by 1 (staying one day longer) the charges C increase by 12.

9.a.

remember, what we just said about the rate of change ?

it is (result change) / (input change).

between 2010 and 2015

the input changed by +5 (from 2010 to 2015).

the result changed by +6.25 (from 37 to 43.25).

the rate of change is therefore

6.25/5 = 1.25 = 1 1/4 = 5/4

the function is therefore

population in millions = (years since 2010)×5/4 + 37

p = y×5/4 + 37

b.

now we want to find the number of years (y) so that the result of that equation is 50.

50 = y×5/4 + 37

13 = y×5/4

52 = 5y

y = 52/5 = 10.4

so, this will be during the 11th year after 2010 = 2021.

10.

be careful and concentrate.

you see that the sequence goes up 20, when n goes up 5 (and not just 1) ? there was your initial mistake.

a.

again, remember the change rate : it is result change / input change.

so, we have here 20/5 = 4.

so,

C(n) = 4×n + 50

b.

n = 12

C(12) = 4×12 + 50 = 98

c.

now we have C(n), and want to find for which n this is true.

C(n) = 78

78 = 4×n + 50

28 = 4×n

n = 7

after 7 visits the costs are 78.

there are the basic costs of 50 (for n = 0 or 0 visits) and then extra 4 for every visit.

d.

the x-axis is for the number of visits, the y-axis for the costs.

so, the line starts at the point (0, 50), and then passes through the points of the original table (5, 70), (10, 90), (15, 110). and if you want you can calculate the points for higher x (or number of visits).

Kobina sells apple pies for 10gh each.kojo sells beverages for ghc1 each.if kobina sells 23 apple pies and kojo sells 17 beverages,what is the total in sales for both producs combined?​

Answers

Answer:

680

Step-by-step explanation:

Based on the given conditions, formulate:  17  × ( 23  + 17 )  

Calculate the sum or difference: 17  × 40  

Calculate the product or quotient: 680  

get the result: 680

Answer: 680

(Hope this helps can I pls have brainlist (crown)☺️)

Given 4(3x-8)=52 prove x=7
Please help me

Answers

Answer:

4(3x-8)=52

divide both sides by 4

4/4(3x-8)=52/4

3x-8=13

add both sides by 8

3x-8+8=13+8

3x=21

divide both sides by 3

3x/3=21/3

x=7

Step-by-step explanation:

Step-by-step explanation:

4( 3x-8) = 52

12x - 32 = 52

Group all like terms

12x = 52 + 32

12x = 84

Divide both sides by 12

12/12x = 84/12

x = 7

Therefore, x = 7.

Hope it helps. Please mark me brainliest.

Independent Task:
Directions:Write the digit in it's place.

1.) 0.34600
______tenths
______thousandths
______hundred thousandths
______hundredths

2.) 20.00642
_______thousandths
_______hundredths
_______hundredths thousandths



Answers

Answer:

1. tenths = 0.3

   thousandths = 0.346

   hundred thousandths = 0.34600

   hundredths = 0.35

2. thousandths = 20.006

    hundredths = 20.01

   hundred thousandths = 20.00642

Step-by-step explanation:

Hope it helps

What is the name of the process you use to rewrite a quadratic function from standard form into vertex form?

Graphing the transformation
Completing the square
Creating vertex form
Transforming the parent function.

Answers

Answer:

completing the square

Step-by-step explanation:

You can change a quadratic equation from standard form to vertex form by completing the square!

(1 point)
Write the complex number z= -7-10i in polar form: z = r(cos (theta)+ i sin (theta)) where r= and 0 =
The angle should satisfy 0<=theta<=2pi

Answers

Answer:

When a complex number z is written in its polar form,z = r(cos theta + i sin theta), the nonnegative number r is called the magnitude, or modulus, of z.

In mathematics, magnitude is the size of a mathematical object, a property by which the object can be compared as larger as or smaller than other objects of the same kind. More formally, an object's magnitude is an ordering (or ranking) of the class of objects to which it belongs.

I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

amir is buying tickets for the $120 million lottery. If he buys tickets with his brother

Answers

Answer:

$20 million.

Step-by-step explanation:

Amir is buying tickets for the $120 million lotteries. If he buys tickets with his brother, then they will split the money equally. But he is also considering buying tickets with his brother’s four friends, and they will each get

The illustration provided in the question is an example of an inverse variation.

What is an inverse proportion?

When there is an inverse proportion, as one of the variable increases, the other variable decreases. As the number of people who share the money increases, the amount of money each person would get would become smaller.

The formula used to represent inverse proportion is:

y =  k/x

• y = dependent variable

• x = independent variable

• k = constant of proportionality

Here is the complete question: Amir is buying tickets for the  million lottery. If he buys tickets with his brother, then they will split the money equally. But he is also considering buying tickets with his brother's four friends, and they will each get  million. Is this an example of direct, inverse, or joint variation?Joint variationInverse variationDirect variation

To learn more about inverse proportion , please check: https://brainly.com/question/25748643

It took Jasmine 1 day and 4 hours to travel 1,960 miles. What was her average speed in miles per
hour?

Answers

Answer:

it took Jasmine 479 miles per hour

BETWEEN WHAT TWO INTEGERS IS THE SECOND ZERO?

Answers

Answer:

between 2 and 3

Step-by-step explanation:

see how it crosses the x axis a little after 2, so it's between 2 and 3

Susie catches 15 butterflies and lets 6 butterflies go for three days in a row

Answers

What is she doing with the butterflies she kept…..

Answer:

Sorry don't report pls I need the points

Step-by-step explanation:

you want to frame a photo from your trip to send home selective frame that suitable for a photo with a perimeter of 70 cm​

Answers

Points H=Mc3
26/861639+owuoe

The total cost of going to the theatre for 18 people is £803.16.

How much will each person need to pay to cover the total cost?

Answers

803.16 divide by 18 = £44.62

For exercises 7-9 write expressions for the area of each rectangle in two different ways. Then find the area using each expressions.

Answers

Answer:

No Questions are shown here

Step-by-step explanation:

Just says "For exercises, 7-9 write expressions for the area of each rectangle in two different ways. Then find the area using each expression."

C*C*C=???
helpp me with this

Answers

Check the picture below.

What is 4a I will give brainiest to whoever’s is first

Answers

4A is ( 4 times A )which will ultimately turn out to A being a number of some sort or cancelled out depending on the problem

Suppose all counting numbers are arranged in columns as shown below. Under what letter will the number 2019 appear?

Answers

Answer: b

Step-by-step explanation:

The population of a city decreases by 1.1% per year. If this year's population is
79,000, what will next year's population be, to the nearest individual?

Answers

Answer:

Step-by-step explanation:

100% - 1.1% = 98.9% = 0.989

79000(0.989)¹ = 78,131

or

1.1% = 0.011

79000(0.011) = 869

79000 - 869 = 78,131

Which expression is equivalent to (1/square root y)^-1/5

Answers

Answer:

y^(1/10).

Step-by-step explanation:

(1/√y)^-1/5

= (y ^-1/2)^-1/5

= y^(-1/2 * -1/5)

= y^(1/10)

Answer:

Step-by-step explanation:

(1/sqrt(y) )^-1/5      To get rid of the minus, turn the sqrt(y) over.

(sqrt(y))^1/5           Represent the square root of y as y^(1/2)

(y^(1/2))^(1/5)         Multiply the powers

y ^ 1/10

What is the slope of the line x=6

Answers

Answer:

undefined

Step-by-step explanation:

Vertical lines never have a defined slope as you can never divide a number by zero

The equation of a line in standard form is:

y

=

m

x

+

b

Where

m

is our slope

b

is our y-intercept

In our case we are only given

x

=

6

x

=

6

is a vertical line therefore the slope is undefined.

HIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

Answers

Answer:

The x-intercept is a point on the x-axis where the line crosses the x-axis and you can easily find it at point (-7, 0) because the line crosses the x-axis there.

Similarly, the y-intercept is a point on the y-axis where the line crosses the y-axis and you can easily find it at point (0, 2) because the line crosses the y-axis there.

The books have been sorted into fiction and nonfiction. The number of fiction books is 5 less than 4 times the number of nonfiction books. The books are 70% fiction. Choose the equation that best represents this scenario.
x over quantity 4 times x minus 5 end quantity equals 30 over 100
x over quantity 4 times x minus 5 end quantity equals 30 over 70

Answers

The number of fiction books are 7 and number of non fiction books are 3 respectively

let

number of fiction books = x

number of non fiction books = y

x = 4y - 5

Total books = z

x = 70% of z

y = 30% of z

x + y = z

4y - 5 + 30%(z) = z

4y - 5 + 0.3z = z

4y - 5 = z - 0.3z

4y - 5 = 0.7x

4y - 5 = 0.7z

4(0.3z) - 5 = 0.7z

1.2z - 5 = 0.7z

-5 = 0.7z - 1.2z

-5 = - 0.5z

z = -5/-0.5

z = 10

Therefore,

the number of non fiction = 30% of z

= 0.3 × 10

= 3

number of fiction = 70% of z

= 0.7 × 10

= 7

Learn more about equation:

https://brainly.com/question/16450098

A taxi service charges $1.00 for the first 1/10 of a mile and $0.10 for each additional 1/10 of a mile after that. fill in the table.
distance traveled

(miles)
9/10
2
3 1/10
10
price
?
(dollars)
Is this a proportional relationship?

Type yes or no

Answers

9414 1404 393

Answer:

  $1.80, 2.90, 4.00, 10.90

  not proportional

Step-by-step explanation:

For some distance d, we have a charge f(d) that is ...

  [tex]f(d)=\begin{cases}1.00&0\le d\le0.1\\1.00+0.10\cdot\dfrac{(d-0.1)}{0.10}&0.1<d\end{cases}[/tex]

for d > 0.1, this simplifies to d +0.9.

Then the charges are ...

  [tex]\begin{array}{cc}\underline{\text{miles}}&\underline{\text{charge}}\\9/10&1.80\\2&2.90\\3\ 1/10&4.00\\10&10.90\end{array}[/tex]

The different relation for the first 1/10 mile indicates ...

  the relationship is not proportional.

Which equation shows y=3x−15 in standard form?

5x−15y=−1

5x−15y=1

15x+5y=−1

15x−5y=1

Answers

Answer:

c  5x -15y =1

5x-15y=1

-5x -15y= 1 -5x     change the signs on both sides of the equation

    15y = -1 +5x      divide both sides by 15

        y = -1/15 + 1/3 x    Reorder the terms

        y = 3x-15

Step-by-step explanation:

Hope this helps:)

Find the inverse function of f informally.

Answers

Answer:

What is f?

Step-by-step explanation:

Find the product using formula ...

formula = ( a + b ) ( a - b )

a) 1.2 × 2.8​​

Answers

Step-by-step explanation:

1.2 × 2.8

(2 - 0.8 )(2 + 0.8)

2² - (0.8)²

4 - 0.64

3.36

Solution:

[tex]\begin{gathered}1.2 \times 2.8 \\ = (2 - 0.8)(2 + 0.8) \\ = {(2)}^{2} - {(0.8)}^{2} \\ = 4 - 0.64 \\ = 3.36\end{gathered}

[/tex]

Answer:

3.36

Hope it helps.

Do comment if you have any query.

Find the values of x, y, and z angle measurements

Answers

X=40 y=100 x=40 I think

What is 2346 to the power of 3?

Answers

Answer:

12911717736

Step-by-step explanation:

"236" to the power of 3 is the same thing as multiply 236 by itself 3 times.

236 · 236 · 236 55696 · 236 12911717736

Therefore, the answer is 12911717736.

Answer:

12911717736

Step-by-step explanation:

You're basically multiplying 2346 by itself 3 times which is why you get 12911717736

1. A cylindrical jar has a radius of 5 inches and a height of 9 inches. The jar is filled with marbles that have a volume of 20 in3. Use 3.14 for pi. Show work. Complete sentences.
a. What is the volume of the jar?









b. How many whole marbles can fit in the jar?
who ever gets the right answer will get brainliest ;)

Answers

Answer:

a. Volume = π15.02 9.0=6361.73

b. I am very sorry, I don't know

Step-by-step explanation:

Need help !! From mathematics only

Answers

Answer:

1) 9h² - 3h + 2h² when h= -1

11h²- 3h

11(-1)²-3(-1)

11+3

14

2) -6m + 3t +2m² when m= 3 and t=-1

-6( 3) +3(-1)+2(3)²

-18 -3 +18

-3

3) 7g² - 2c³/ 3g - c² when g=2 and c= -1

7(2)² - 2(-1)³ / 3(2) - (-1)²

28 +2 / 6-1

30/5

6

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