The directrix of a parabola is y = 4. Its focus is (2,6).

What is the standard form of the parabola?

Answers

Answer 1

Answer:

Step-by-step explanation:

The Directrix Of A Parabola Is Y = 4. Its Focus Is (2,6).What Is The Standard Form Of The Parabola?
Answer 2

The standard form of parabola having vertex ( 2 , 5) is given by y = [tex]\frac{1}{4}[/tex] ( x - 2 )² + 5.

What is a parabola ?

A parabola is a plane curve that is produced when a point moves so that its distance from a given point equals its distance from a fixed line.

We know that , the standard form or general equation of a parabola is given by :

y  = a ( x - h )² + k

where : vertex is (h, k) and focus ( h , k + p)

We know that here directrix is y = k - p and a is a = [tex]\frac{1}{4p}[/tex]

It is given that focus is (2 , 6).

From focus :

h = 2 and k + p = 6

whereas from directrix :

k - p = 4

Adding both

k + p = 4

k - p = 6

We get :

2k = 10

or

k = 5

So ,

p = 1

And vertex will be :

(h , k) = (2 , 5).

The vertical distance from vertex to directrix p = 1 :

y  = a ( x - 2 )² + 5

here , a = [tex]\frac{1}{4p}[/tex] or a = 1/4

So , the standard form of given parabola will be :

y = [tex]\frac{1}{4}[/tex] ( x - 2 )² + 5

Therefore , the standard form of parabola having vertex ( 2 , 5) is given by y = [tex]\frac{1}{4}[/tex] ( x - 2 )² + 5.

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Related Questions

Can you help me? Thanks!

Answers

Answer:

the answer is here

Step-by-step explanation:

180- 68

=112

Find the measure of angles 1,2 and 3

Answers

Answer:

??

Step-by-step explanation:

where is the question

If f(x) = x and g(x) = X + 2, which statement about the graphs of the functions is true?
A. g is a translation of f 2 units down.
B. g is a translation of f 2 units to the right.
C. g is a translation of f 2 units to the left and 2 units down.
D. g is a translation of f 2 units up.
PLEASE HELP ME DUE IN 10 minutes!!!

Answers

Answer: D

Step-by-step explanation: +2 would be an upwards translation

Please hwlp! Ava is driving her car. At the end of 2 hours she has driven 92 miles, and at the end of 5 hours she has driven 245 miles. What is her average rate of change?
_(blank)_ miles per hour

Answers

Answer: 51 miles per hour

Use the points (2,92) and (5,245)
Then do y2-y1/x2-x1
So 245-92/5-2
=153/3
Simplify= 51

solve the question, thank you

Answers

Answer:

A . m = 11/6

its going to be a

the answer is A because when you do y2 - y1 / x2- x1 you are doing 18-7/ 4- (-2) and 18-7 is 11 and 4-(-2) is 6 so your answer will be 11/6 which is A

Which value of x makes this equation true? 35 + 42 = 12 + x​

Answers

Answer:

65

Step-by-step explanation:

So let's first set up our equation here:

35 + 42 = 12 + x

Now, let's add like terms

77 = 12 + x

Now, let's subtract both sides by 12

65 = x

Answer:

x=63

Step-by-step explanation:

35+42= 75

75-12= 63

4m-3(m +2) what is the answer step by step​

Answers

Answer:

-1m-6

Step-by-step explanation:

1. Multiply -3*m = -3m

2. Multiply -3* 2 = -6

3. Combine like terms : 4m + -3m = -1m

4. -1m - 6

To change Celsius temperatures to Fahrenheit temperatures, you can use the formula F = 95C + 32. Which answer is the best first step to solve the equation for C?

Answers

Answer: I think that the guy above is right just subtract 32.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The first step in solving the equation for C is

Subtract 32 on both sides.

F - 32 = 95C + 32 - 32

F - 32 = 95C

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example:

2 + 3x + 4y = 7 is an expression.

We have,

To change Celsius temperatures to Fahrenheit temperatures, you can use the formula F = 95C + 32.

Solve for C.

F = 95C + 32

Step 1:

Subtract 32 on both sides.

F - 32 = 95C + 32 - 32

F - 32 = 95C

Divide both sides by 95.

(F - 32)/95 = C

C = (F - 32) / 95

Thus,

The first step in solving the equation for C is

Subtract 32 on both sides.

F - 32 = 95C + 32 - 32

F - 32 = 95C

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Help please! Explain it to me. And give an idea to create ​

Answers

Answer:

You could design a solar panel.

Step-by-step explanation:

Nature uses sunlight to grow and provide food for animals, but it only uses what it needs. And it forms a function. So by designing a solar panel, you imitate the way nature works. Solar panels only soak in sunlight for energy when it needs it, which is a function that provides electricity.

(What the question is asking is that you design a product in which some of the aspects listed would be imitated)

Brody had his computer repaired at Store A. His bill was:
Initial Repair Cost = $1,200
Sales Tax of 6 percent = $72.00
Gratuity of 15 percent
Explain how you would calculate the gratuity for the
services provided.

Answers

Answer:

Add the repair cost and tax to get the total amount. Then multiply the total amount by 0.15 to find the gratuity.

Step-by-step explanation:

This is sample response

The gratuity for the services provided is $190.8 if the Initial Repair Cost = $1,200, the Sales Tax of 6 percent = $72.00, and the Gratuity of 15 percent.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Brody had his computer repaired at Store A. His bill was:

Initial Repair Cost = $1,200

Sales Tax of 6 percent = $72.00

A gratuity of 15 percent

Total cost = 1200 + 72 = 1272

The gratuity for the services provided = 0.15x1272 = $190.8

Thus, the gratuity for the services provided is $190.8 if the Initial Repair Cost = $1,200, the Sales Tax of 6 percent = $72.00, and the Gratuity of 15 percent.

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10x+36-38x-47 I don't understand this question i am so confused please explain i would be really thankful.

Answers

-28x-11

Step-by-step explanation:

10x-38x=-28x

+36-47=-11

so the answer is -28x-11

How many solutions for the equation, 8x - 19 = -4 -7x

Answers

Answer: One.

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :   8*x-19-(-4-7*x)=0

Pull out like factors :   15x - 15  =   15 • (x - 1)

 Solve :    15   =  0

Solve  :    x-1 = 0  

 Add  1  to both sides of the

x2-6x+3 can be written in the form of (x+m)2 +n find the value of m and n

Answers

Answer:

2(x-3x) + 3

value of X and M is x and -3x respectively

Step-by-step explanation:

you can factor out the 2 from the 2x -6x and gets the 2(x-3x) while n is the constant that remains the value of 3

I hope this helps

Answer:

m = - 3, n = - 6

Step-by-step explanation:

Expand and compare coefficients of like terms, that is

(x + m)² + n

= x² + 2mx + m² + n

Compare to x² - 6x + 3

comparing coefficients of x- term

2m = - 6 ( divide both sides by 2 )

m = - 3

Comparing constant terms

m² + n = 3 , that is

(- 3)² + n = 3

9 + n = 3 ( subtract 9 from both sides )

n = - 6

a line passes through the point (-6,4) and has a slope of 5/2

Answers

The equation in slope intercept for is y = 5/2x + 4

The y intercept is 4

Elena is playing a dice game with her father. She will win if she DOES NOT roll a 1, 3, or 6. Find the probability that Elana wins on her next roll.

Answers

Answer:

The probability that she was on her next roll is 1/2

Step-by-step explanation:

If she does not roll 1,3 or 6, she wins

So if she rolls 2,4 and 6 , she wins

The probability of rolling each is 1/6 each

So the probability of rolling any of the three will be:

1/6 + 1/6 + 1/6 = 3/6 = 1/2

Which of the following is equivalent to -(7/4) ?

A. 7/-4



B. -7/-4



C. 4/-7



D. 7/4

Answers

Answer:

A

Step-by-step explanation:

-(7/4) equals -7/4 or negative seven forths. Its doesn't matter where the negative sign is as long there's only 1 of them and that its still 7/4.

So through process of elimination, we take out B because theres 2 negative, which make a positive, our answer is negative

C is wrong because its 4/7, not 7/4

D is wrong because it's positive, leaving us with A

If a train travels 1,600 km in 16 hours, how fast is it moving?

Answers

Answer:

100km per hour

Step-by-step explanation:

16/16= 1 hour

1600/16= 100

Math question:
In ΔRST, m

Answers

Answer:

huh i dont understand can u post a pic

It takes Taylor hour to make of a batch of cookies. About how long will it take him to make 8 batches?


A.

1.1 hours

B.

3.6 hours

C.

5.4 hours

D.

7.2 hours

Answers

Answer:

7.2 I think, closest to 8 hours?

Write the algebraic notation for dilation with a scale factor of ½

Answers

Answer:  (x, y) goes to (1/2x, 1/2y)

Step-by-step explanation:

What is the slope of the line 4x-2y=5

Answers

Answer:

slope = 2

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Edgen 2023

Compare the numbers

Answers

Answer:The answer is ≥ greater than or equal to

can you mark me Brainliest please

Adam Levine wants to buy a new outfit for the Voice. The suit he wants is priced at $300
but it is on sale for 22% off. What discount would Adam get if he buys the suit?
He would get a discount of $

HELP!

Answers

Answer:

66 bucks

Step-by-step explanation:

take 300 and 22% then subtract that answer from 300.

Find the square root of 36 by prime factorisation
method​

Answers

Answer:

36

2×18

2×9×2

2×2×3×3

=> square root of 36 =6

Q

H.

The two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:

Step

Statements

Reasons

1

UV || WZ

Given

2

Points S. Q, R, and T all lie on the same line.

Given

3

mZSQT = 180°

Definition of a Straight Angle

Angle Addition Postulate

4

m2SQV + m2VQT = m_SQT

5

Substitution Property of Equality

6

m2VQT + mZZRS = 180°

Same-Side Interior Angles Theorem

Substitution Property of Equality

7

m2SQV+mZVQT = m2VQT + mZZRS

Answers

Answer:

i can't understnd it at all i mean you organized it but what does those mean??

Step-by-step explanation:

Choose a system of equations with the same solution as the following system:
4x − 2y = 6
2x + y = 5

A) −4x − 2y = 10
2x − 3y = 21

B) 4x + 2y = 10
10x + y = 21

C) −4x − 5y = −1
2x − 6y = 10

D) 3x + 2y = 6
9x + y = 17

Answers

Answer:

The answer is C.

Answer:

the answer is C

Step-by-step explanation:

I took the test

Which expression is equivalent to (3w−8)−4(2w+3)

Answers

Answer:

-5w -20

Step-by-step explanation:

(3w-8) -4(2w+3) start by removing the parentheses

3w-8-4(2w+3)

-5w-8-12 collect like terms

-5w-20 and that's how you get the answer

Tell me which ones are greater than or lesser than with these <>?

Answers

Answer:

1. >

2.<

3.<

btw

Absolute value equations are equations where the variable is within an absolute value operator, like |x-5|=9. The challenge is that the absolute value of a number depends on the number's sign: if it's positive, it's equal to the number: |9|=9. If the number is negative, then the absolute value is its opposite: |-9|=9.

Which expression does the number line represent?

NA

0

1

4

2

4

3

4

9

5

4

6

4

7

4

4

8

4

ده

9

Save and Exit

Next

Sun

Answers

Answer: D) 9 Over 4 divided by three-fourths

Step-by-step explanation:

The number line shown below is divided into 3 equal parts. To do so the highest number would have to be divided by a number that would give 3 as an answer.

Say that number is x;

x = (9/4) / 3

= 0.75

= 3/4

Number line shows 9 Over 4 divided by three-fourths .

Need help will mark brainliest

Answers

Answer:

AB≅AC  (two legs of isosceles triangles are always equal)

6x-14 = 4x+20

2x-14 = 20

2x = 34

x = 17

Base ⇒ 7x-12

           = 7(17)-12

           = 119-12

           = 107

Answer:

x=17, 107

Step-by-step explanation:

Since it is given that the triangle is isosceles, we can make the following equation:

6x-14=4x+20

x=17

To find the base (7x-12), all you have to do is plug in the value of x

7x-12

7*12-12

107

I hope this helps :)

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