what eqwation of a parabola with a focus(6,-2) and a directrix x=-2

Answers

Answer 1

Answer:

The equation of the parabola

( y +2 )² = 16 (x-2)

Step-by-step explanation:

Step(i):-

Given the focus of the Parabola ( 6, -2 )

we know that the Focus of the Parabola

                ( h + a , k ) = ( 6 , -2 )

Comparing

              h + a = 6 ...(i)

          and  k = -2

Given directrix of the parabola

           x = -2

The  directrix of the parabola  x = h - a = -2

        h - a = -2 ...(ii)

Adding (i) and (ii) equations , we get

    h + a + h-a = 6 -2

                2 h = 4

           ⇒    h  = 2

Substitute 'h' = 2 in equation (i) , we get

          h + a = 6

          2 + a = 6

                a = 6 -2 =4

Step(ii):-

The equation of the parabola having Vertex ( h,k) = (2 , -2) and a = 4

[tex](y-k)^{2} = 4a ( x-h)[/tex]

( y - (-2))² = 4 (4) ( x -2)

Final answer:-

The equation of the parabola

[tex](y-(-2))^{2} = 4(4) ( x-2)[/tex]

( y +2 )² = 16 (x-2)


Related Questions

Maria can paint an area of 100 square feet in one-third of an hour. At this rate, how
many square feet can she paint in one minute?

Answers

Answer:

A.    5 square feet per minute

Step-by-step explanation:

Answer:

The answer is 5 square feet per minute.

Step-by-step explanation:

Since 1/3 of an hour is 20 minutes, it will look like 100 square feet/20 min.

To make 20 minutes into one minute, we have to divide it by 20.

Because we did it to the denominator, we also have to do the same thing to the numerator.

Divided 100 by 20, which gives you 5.

Hope this helps!!

Domain and Range for the function f(x)=5IXI is

Answers

Answer:

The domain of the function f(x) is:

[tex]\mathrm{Domain\:of\:}\:5\left|x\right|\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

The range of the function f(x) is:

[tex]\mathrm{Range\:of\:}5\left|x\right|:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}[/tex]

Step-by-step explanation:

Given the function

[tex]f\left(x\right)=5\left|x\right|[/tex]

Determining the domain:

We know that the domain of the function is the set of input or arguments for which the function is real and defined.  

In other words,  

Domain refers to all the possible sets of input values on the x-axis.

It is clear that the function has undefined points nor domain constraints.

Thus, the domain of the function f(x) is:

[tex]\mathrm{Domain\:of\:}\:5\left|x\right|\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

Determining the range:

We also know that range is the set of values of the dependent variable for which a function is defined.  

In other words,  

Range refers to all the possible sets of output values on the y-axis.

We know that the range of an Absolute function is of the form

[tex]c|ax+b|+k\:\mathrm{is}\:\:f\left(x\right)\ge \:k[/tex]

[tex]k=0[/tex]

so

Thus, the range of the function f(x) is:

[tex]\mathrm{Range\:of\:}5\left|x\right|:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}[/tex]

A candy company puts 4 gumdrops each bag. how many gumdrops will the company need to fill 3,873?

Answers

Answer:

15,492 gumdrops

Step-by-step explanation:

If the company needs 3,873 bags of candy and each bag has 4 pieces of candy it them, then multiply the amount of bags they need and the amount in each bag and you will get how many they need in total.

MARKING BRAINLIST!!! In a couplet one statement is _____ and one is ______
A. Agreeing and rejecting
B. Deciding and Acting
C. Informing and Agreeing

Answers

Deciding and Acting.

A couplet can have an open sentence which is the deciding and the closing sentence being the acting.

Find the equation of the exponential function represented by the table
below:
2
y
0
1
1
2
2
4
3
8.

Answers

9514 1404 393

Answer:

  y = 2^x

Step-by-step explanation:

The x-values are sequential integers, which helps the discovery of the function. The y-values have a common ratio of 2 = 2/1 = 4/2 = 8/4. This is the base for the exponential function.

The initial value of y=1 at x=0 tells you the multiplier of the exponential factor is 1, and the exponent is x (with no additions or subtractions). Your function is ...

  y = 2^x

WILL MARK BRAINLIST!!! only for correct answer
NEED CORRECT ANSWER ASAPPP

Answers

Answer:

C.11

Step-by-step explanation:

By drawing the line of best fit (using the other points) you can estimate how long 14 rows will take, which is 11 minutes.

I need help and for the other select it’s are or are not

Answers

Answer:

Step-by-step explanation:

It's clear from the graph that the angles of the given triangles are different.

And for similarity of two triangles, at least two angles of the triangles should be congruent.

Therefore, both the triangles are not similar.

The angles are DIFFERENT.Since similarity transformations preserve angle measures, ΔUVW and ΔGHI ARE NOT similar.

Help what’s the answer?

Answers

Answer:

what are you ment to do...............

How many 1/ 4-inch cubes does it take to fill a box with width 2 1/ 4 inches, length 2 1/ 2 inches, and height 1 3/ 4 inches?

Answers

Answer:

630.

Step-by-step explanation:

Given the following data;

Dimensions for cube = ¼ inches

[tex] Volume \; of \; cube = \frac {1}{4} * \frac {1}{4} * \frac {1}{4} [/tex]

Volume = 1/64 cubic inches.

For rectangular box;

Length = 2½ = 5/2 inches.

Width = 2¼ = 9/4 inches.

Height = 1¾ = 7/4 inches.

[tex] Volume \; of \; cube = \frac {5}{2} * \frac {9}{4} * \frac {7}{4} [/tex]  

Volume = 315/32 inches

Therefore, to find the amount of cubes;

[tex] Number \; of \; cubes = \frac {Volume \; of \; box}{Volume \; of \; cube} [/tex]

Substituting into the equation, we have;

[tex] Number \; of \; cubes = \frac {\frac {315}{32}} {\frac {1}{64}} [/tex]

[tex] Number \; of \; cubes = \frac {315}{32} * 64 [/tex]

[tex] Number \; of \; cubes = 315 * 2 [/tex]

Number of cubes = 630

Solve the following inequality.
8x-1<15

Answers

Answer:

x < 2

Step-by-step explanation:

I hope this help you

Solve by elimination.
2x + 8y = 60
5x + 4y = –10

Answers

Answer:

2x + 8y = 60= 30

5x + 4y = –10= -2

Step-by-step explanation:

Simplifying

2x + -8y = 60

Solving

2x + -8y = 60

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '8y' to each side of the equation.

2x + -8y + 8y = 60 + 8y

Combine like terms: -8y + 8y = 0

2x + 0 = 60 + 8y

2x = 60 + 8y

Divide each side by '2'.

x = 30 + 4y

Simplifying

x = 30 + 4y


HELP PLS!! I need help for question 10, answers a, b, and c! (Everything is in the picture)

Answers

Answer:

A. The line on the left

B.not sure

C. 20 dollars

Step-by-step explanation:

Analyze the drawing.The beam in the mobile is balanced.The cups on the right and left are equal,which means the the items can be removed and mobile still balances.This leaves 4 circles on the left,a cup and 1 circle on the right.Now the circle on the right cancels out the circle on the left,leaving three circles on the right.The logical conclusion is that the cup is equal to 3 circles

Answers

Answer:

See the attached

Step-by-step explanation:

Solution is given on the picture

What is the image point of (-7,7) after a translation right 1 unit and down 3 units?

Answers

Answer:

(-6,4)

Step-by-step explanation:

-7-(-1)=-6

7-3=4

Need help asap please

Answers

Answer:

Multiply four on both sides

Step-by-step explanation:

;)

PLEASE HELP THE ANSWER HAS TO BE A INTEGER OR A DECIMAL.

Answers

Answer:

It's the same as the last one. The answer is -2.3

Step-by-step explanation:

Which expression is a factor of both x^2-9 and x^2+8x+15

Answers

Step-by-step explanation:

x^2-9=0x^2+8x+15=0

(x+5)(x+3)=0

x+5=0 or x+3=0

x=-5or x=-3

x=-5 in x^2-9=0

(-5)^2-9=0

10-9=0

1=0

x=-3 in x^2-9=0

(-3)^2-9=0

9-9=0

0=0

A multiple choice quiz has two questions , each with five answer choices. Only one choice is correct. Find the probability of answering two questions correctly,
. Show work

Answers

Answer:

1/25 to get both correct

Step-by-step explanation:

So the probability of getting one choice correct is 1/5

Since 5 choices 1 is correct

now we have to get 2 in a row correct so

1/5*1/5=1/25

Please help me i struggle lots on this topic

Answers

Answer:

slope = 0

Step-by-step explanation:

remember slope is just rise (change in y) over run (change in x) and since there's no change it has a zero slope, which applies to any horizontal line parallel to the x axis

(this is just me trying to explain slopes, separate from the question you put) if the right most point was 1 higher (5,7) instead of (5,6) then the slope would be 1/2 because to get from (5,7) to (3,6) you move up 1 and over 2

what is a fraction
what is a half
what is 0.5​

Answers

Answer:

1.what is fraction?

A.a numerical quantity that is not a whole number (e.g. 1/2, 0.5).

2.what is a half?

A.either of two equal or corresponding parts into which something is or can be divided.

"two and a half years"

3.what is 0.5?

A. 0.5=½

Put simply, a fraction is a numerical quantity that is not a whole number.

For example: 1/4 is literally interpreted as 1 divided by 4, or 1 ÷ 4.

A half is just a number that is equal 0.5 which is equal to 1/2

Sub to oTechz :)

Can someone plz help me. There is an equation and the cost too.

Answers

Answer:

C = 40p

Cost for 15 people: 600 dollars

Step-by-step explanation:

The amusement park charges $40 per person.

That can be represented as 40 × P or 40P.

C is equal to the cost of admission for P people.

So, C = 40P

C = 40P

C = 40(15)

C = 600

The cost of admission for 15 people is 600 dollars.

Hope that helps.

y = 3x + 5
y = 4x2 + x

Answers

Answer:

8x and 4x(2) + 5

Step-by-step explanation:

It doesn't make sense but I am pretty sure this is correct

f(x)=3x-5 please help :>

Answers

Answer:

x= 5/3?????

Step-by-step explanation:

try using math

way

(x+y)^4 I am trying to simplify this problem and am kinda confused by it​

Answers

Answer:

This is already as simple as it will get.  You could expand it though.  In that case you'd get:

(x + y)⁴

= (x² + 2xy + y²)²

= x⁴ + 2x³y + x²y² + 2x³y + 4x²y² + 2xy³ + x²y² + 2xy³ + y⁴

=  x⁴ + 4x³y + 6x²y² +4xy³ + y⁴

But this doesn't simplify at all.

A function h(x) is defined by the equation h(x) = sqrt x-2 + 3. Which is the graph of h(x)?

Answers

ExplanationGiven Equation

[tex]h(x) = \sqrt{x - 2} + 3[/tex]

Transformation

A constant inside the square root will make the graph shift either left to right, depending on the number. From the equation. The graph shifts to right two units.

A constant outside the square root will make the graph shift up or down, depending the value. From the equation, the graph shifts up 3 units.

AnswerSecond Image, the first one where x = 2 and y = 3.

Answer:

Step-by-step explanation:

second graph

anyone wanna have a conversation

Answers

Answer:

sure

Step-by-step explanation:

Answer:

hii

Step-by-step explanation:

A small software development company invests $16,000 to produce a software package that will sell for $50.65. Each unit costs $8.20 to produce. How many units must the company sell to break even? How many units must the company sell to make a profit of $95,000?

Answers

Answer:

376 units and 1,857 units

Step-by-step explanation:

The computation is shown below:

The number of units that company sells to break even is

Let us assume the number of units be x

$16,000  + $8.20x  = $50.75x

$16,000 = $50.75x - $8.20x

$16,000 = $42.55

x = $16,000 ÷ $42.55

= 376 units

Now in order to make the profit the number of units sold is

$50.65x - ($16,000 + $8.20x) = $95,000

$50.65x - $16,000 - $8.20x = $95,000

$42.55x = $95,000 - $16,000

$42.55x = $79,000

x = $79,000 ÷ $42.55

= 1,857 units

Determine if the following expressions are equivalent. If so, by what property are they equivalent.

3(x-2) and 3x - 6

A. yes, by associative property
B. yes, by commutative property
C. yes, by distributive property
D. no, the expressions aren't equivalent.

Answers

Answer:

C. Yes, by distributive property

Step-by-step explanation:

Distributive property states that 3 can be distributed to all of the terms inside of the parentheses, namely x and -2. 3x + 3(-2) = 3x-6

2 1
3 4
- 그
Is this addition or division

Answers

The answer is to this problem is 4/12

Salvador sold hats during the weekend sporting event. On Saturday, Salvador sold ( * of the total number of hats. On Sunday, he sold & ( of the total number of hats. What fraction of the total number of hats was left over?

Answers

Answer:

5/28

Step-by-step explanation:

Salvador sold hats during a weekend sporting event. On Saturday, Salvador sold 4/7 of the total number of hats. On Sunday, he sold 1/4 of the total number of hats. What fraction of the total number of hats was left over

Total number of hats = x

Hats sold on Saturday = 4/7x

Hats sold on Sunday = 1/4x

Hats left over = x - (4/7x + 1/4x)

= x - ( 16x+7x/28)

= x - 23/28x

= 28x - 23x/28

= 5/28x

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