The directrix of a parabola is y = 4. Its focus is (2,6).
What is the standard form of the parabola?
Answers
Answer:
Step-by-step explanation:
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
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
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
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
Can you help me? Thanks!
Answers
Answer:
the answer is here
Step-by-step explanation:
180- 68
=112
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
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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Find the measure of angles 1,2 and 3
Answers
Answer:
??
Step-by-step explanation:
where is the question
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 .
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.
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.
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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Compare the numbers
Answers
Answer:The answer is ≥ greater than or equal to
can you mark me Brainliest please
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)
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
Find the square root of 36 by prime factorisation
method
Answers
Answer:
36
2×18
2×9×2
2×2×3×3
6²
=> square root of 36 =6
Math question:
In ΔRST, m
Answers
Answer:
huh i dont understand can u post a pic
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
solve the question, thank you
Answers
Answer:
A . m = 11/6
its going to be a
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 :)
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
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?
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:
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
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 y intercept is 4
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
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
Use the points (2,92) and (5,245)
Then do y2-y1/x2-x1
So 245-92/5-2
=153/3
Simplify= 51
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 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
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: