Use the given information to write the equation of the parabola.

Vertex: [tex](0,0)[/tex]
Focus: [tex](0,-\dfrac{1}{2})[/tex]

Answers

Answer 1

Answer:

x² = -2y

Step-by-step explanation:

The focus is p away from the vertex, and so is the directrix.

To find the equation of the parabola, we must first determine if the parabola is horizontal or vertical.

Horizontal parabola [Standard form]: (y – k)² = 4p(x – h)Vertical parabola [Standard form]: (x – h)² = 4p(y – k)

If the parabola is vertical, the directrix, and focus will have the same x value but different y value compared to the vertex (h, k). You can also tell if the directrix in in the form y = k – p, and if the focus is in the form (h, k + p).

Likewise, if the parabola is horizontal, the directrix, and focus will have the same y value but different x value compared to the vertex (h,k) . You can also tell if the directrix is in the form x = h – p, and if the focus is in the form (h + p, k).

For this problem, given that the vertex is at the origin (0,0), and that the focus is at the point (0, -½).

You can tell that the x value is the same for the vertex, and focus so this must be a vertical parabola. Because this is a vertical parabola, we can use the form mentioned as earlier (x – h)² = 4p(y – k).

If h = 0, and k = 0, the p value must be the difference between the k of the vertex, and the k of the focus: -½ - 0 → -½.

Now we can just plug in our known information to derive the equation!

h = 0, k = 0, p = -½ → (x - h)² = 4p(y - k) →

(x - 0)² = 4(-½)(y - 0) → x² = -2(y - 0) →

x² = -2y.

Also p = 1/4a, if you are wondering.

So because this is a vertical parabola, x² = -2y is generally the same as y = -1/2x² in standard quadratic form. I just like to think of the horizontal parabola as an inverse quadratic because it is like reflecting over the line y = x.

Answer 2

Answer:

[tex]\boxed {\boxed {\sf x^2=-2y}}[/tex]

Step-by-step explanation:

First, plot the two points. We can see the focus is below the vertex. The result will be a vertical parabola. Since the parabola must contain the focus, it will have to open downward.

From this information, we know that the following equation must be used:

[tex](x-h)^2=-4p(y-k)[/tex]

where (h,k) is the vertex and p is the distance from the focus to the vertex.

Next, find p, the distance between the focus and vertex. We can use the distance formula.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The vertex is (0,0) and the focus is (0, -1/2). Therefore:

[tex]x_1=0\\y_1=0\\x_2=0\\y_2= -1/2[/tex]

[tex]d=\sqrt{(0-0)^2+(0--1/2)^2}[/tex]

[tex]d=\sqrt{(0)^2+(0+1/2)^2}[/tex]

[tex]d=\sqrt{0+(1/2)^2}[/tex]

[tex]d=\sqrt{0+1/4}[/tex]

[tex]d=\sqrt{1/4}[/tex]

[tex]d=1/2[/tex]

Now we know the distance and vertex. We can plug the values into the equation.

d=1/2 and (h,k)= (0,0)

[tex](x-0)^2=-4(1/2)(y-0)[/tex]

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

[tex]x^2=-2y[/tex]

The equation of the parabola is x²= -2y

Use The Given Information To Write The Equation Of The Parabola.Vertex: [tex](0,0)[/tex]Focus: [tex](0,-\dfrac{1}{2})[/tex]

Related Questions

The temperature of a liquid in an experiment starts at 0 degrees Celsius. The experiment calls for the temperature of the liquid to change at a rate of –0.6 degree Celsius per minute. How long will it take for the liquid to reach –10.5 degrees Celsius? 2Points Remember to divide to find the minutes.

Answers

Answer:

It will take 17.5 minutes or 17 minutes and 30 seconds to reach -10.5 degrees celsius

Step-by-step explanation:

Starting at 0 degrees, we have a change of -0.6 degree celsius per minute

We want to know how long it will take for the liquid to reach - 10.5 degrees Celsius

The total difference between the two is;

-10.5 - 0 = -10.5

The change per minute is -0.6

So the number of minutes it will take will be;

-10.5/-0.6 = 17.5 minutes

A point is chosen in the circle at random. Determine which of the statements are true. Check all that apply.
It is unlikely the point is in region A.
It is likely the point is in region C.
It is likely the point is in region G.
It is impossible for the point to be in region H.
It is certain that the point will land in a lettered region.

Answers

a,d,e

Step-by-step explanation:

I took the question

Answer:

A D E

Step-by-step explanation:

সৌরজগতের গ্রহ গুলোর চিএসহ বননা দাও​

Answers

Answer:

সৌরজগতে গ্রহগুলির ক্রম, সূর্যের নিকটতম সূচনা এবং বাইরের দিকে কাজ করা নিম্নরূপ: বুধ, শুক্র, পৃথিবী, মঙ্গল, বৃহস্পতি, শনি, ইউরেনস, নেপচুন এবং তারপরে সম্ভাব্য প্ল্যানেট নাইন। আপনি যদি প্লুটোকে অন্তর্ভুক্ত করার জন্য জেদ করেন তবে তা নেপচুনের পরে তালিকায় আসবে

আশাকরি এটা সাহায্য করবে

Given the function f ( x ) = − 1 x + 3 x 4 , f(x)=− x 1 ​ + 4 3 x ​ ​ , find f ′ ( 4 ) . f ′ (4). Express your answer as a single fraction in simplest form.

Answers

Step-by-step explanation:

The question is not well written. Let us say the function given as expressed as;

f(x) = -1/x + 3/x⁴

f'(x) means we are to differentiate the function with respect to x;

Given f(x) = axⁿ

f'(x) = naxⁿ⁻¹

f(x) = -x⁻¹ + 3x⁻⁴

Applying the differentiation formula we will have;

f'(x) = -1(-x⁻²)+(-4)3x⁻⁴⁻¹

f'(x) = x⁻²-12x⁻⁵

Express as a fraction

f'(x) = 1/x²-12/x⁵

To get f'(4), we will have to substitute x = 4 into the resulting expression

f'(4) = 1/4²-12/4(5)

f'(4) = 1/16-12/20

f'(4) = 1/16-3/5

Find the LCM

f'(4) = (5-48)/80

f'(4) = -43/80

Note that the function used was assumed but the same method can be employed to any other functions.

DUE 10:00 PM HELP ASAP. When Sarah left your house this morning her cell phone was 80% charged and then it started to lose 8% charge for each hour there after write an equation for B in terms of tea representing the charge remaining in series battery as percentage t hours after Sara left her house

Answers

Answer:

The answer would be B=-8>80

Step-by-step explanation:

B= 80-8t is the answer

Un ascensor está en el segundo subsuelo, sube
seis pisos, luego baja cinco, vuelve a subir ocho
y finalmente baja trece. /En qué piso se quedó

Answers

Answer:

8th floor

Step-by-step explanation:

Because he went up twice

A certain map shows two roads. Road A is 1 1 2 miles long but is 1 7 8 inches long on the map. What is the unit rate for inches per mile on this map​? If road B is 8 miles ​long, how long is road B on the map​?

Answers

Answer:

a) What is the unit rate for inches per mile on this map?

= 5/4 inches per mile

b) If road B is 8 miles long, how long is road B on the map?

10 inches on the map

Step-by-step explanation:

a) A certain map shows two roads. Road A is 1 1/2 miles long but is 1 7/8 inches long on the map. What is the unit rate for inches per mile on this map​?

Unit rate for inches per mile is calculated as:

1 7/8 inches/ 1 1/2 miles

= 15/8 / 3/2

= 15/8 × 2/3

= 5/4 inches per miles

b) If road B is 8 miles ​long, how long is road B on the map​?

The unit rate is given as:

5/4 inches per miles

Hence,

Road B = 8 miles long

The length of Road B on the map =

5/4 inches per miles × 8 miles

= 10 inches

Which of the following sequences is not a geometric sequence?

50, 25, 12.5, 6.25, …
6, -12, 24, -48, …
0, 2, 4, 6, …
-1, -3, -9, -27, …

Answers

Step-by-step explanation:

the third sequence(0,2,4,6) is not a geometrical sequence

this may help you(:

Answer:

0, 2, 4, 6, …  because the following sequence is arithmetic not geometric

Please Help me find the answer by doing it step by step! PLEASE!!! QUICK!!! THIS IS URGENT!
-3[2- (y - 5] -4 [3 (y + 1) - (6 - y) (-2)]

Answers

Answer:

Standard form:

93−45y

Factored form:

3(31−15y)

I need 4 answers , The cost per pound of the apples on sale is $
.The cost per pound of the apples on sale is $___
.
You can buy
pounds of apples for $18.00 ___
Since 1 pound = 16 ounces, so there are about ___
apples in each pound.
You can buy approximately ____
apples for $18.00.

Answers

I believe the answer would be 18 apples since 1 pound = $1

Can anyone help me out with my Math homework plz and also can you provide step by step explanation of the attachment I will give you 20 points:

Answers

Answer:

y = -x + 2

Step-by-step explanation:

For any linear equation, the equation of the line can be written in the form 'y=mx+c'. In this form, m is the slope and c is the y-intercept. We can figure out both these things using the graph.

The slope is like the incline/decline and can be found by getting two points on the line, say (x1,y1) and (x2,y2) and using the following formula:

m = (y2-y1) / (x2-x1)

So lets take two points: (-1,3) and (2,0)

m = (0-3)/(2-(-1))

m = -3/3

m= -1

The y intercept (c) is the value for x when the line crosses the y-axis.

From the graph we can see that the line crosses the y axis when x=2

∴ c = 2

Now that we know the slope and intercept, we just sub them into the formula:

y = mx +c

y = -x + 2

Let me know if you have questions :)

Answer:

y equals -x plus 2

Step-by-step explanation:

for any linear equation, the equation of the line can be written in the form 'y=mx+c'. In this form, m is the slope and c is the y-intercept. We can figure out both these things using the graph.

the slope is like the incline or decline and can be found by getting two points on the line, say (x1,y1) and (x2,y2) and using the following formula:

                       m = (y2-y1) / (x2-x1)

According to the Woodlawn Park Zoo in Seattle, Washington, the average height
in inches (h) of a baby giraffe during its first week can be described by the
equation h = 72 + 1.2d, where d is the number of days since it was born.
Which statement explains the meaning of the 1.2 in the equation?

Answers

Answer:

the giraffe grows 1.2 inches a day

Step-by-step explanation:

Write a multiplication equation for "Eight $5 bills are worth $40."

Answers

Answer: use your 5 times tables.

Step-by-step explanation:

5, 10 15, 20 25, 30, 35, 40

then count how many times it gotyou to 40

it took 8 times to get to 40.

if -2/5r=-20, then r=50 true or false

Answers

Answer:

true

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

-2/5*50=-20

-2/250=-20

-1/125=-20

I think of a number i halve it then subtract four

Answers

Answer:

x/2-4

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

this question is not very detailed but I think ik what u mean. take a number, 8 for example. halve it, (divide by 2) and then subtract 4 & u are left with 0

The area of a square is (9x2 − 12x + 4) square units. Determine the length of each side of the square by factoring the area expression completely

Answers

Step-by-step explanation:

9x2 − 12x + 4 = 18 - 12x + 4 = 22 - 12x = 2(11 - 6x)

length of 1 side = ± sqrt 2(11-6x) (rej neg value)


Determine whether the graph represents a function

Answers

Answer:

Step-by-step explanation:

18). Graph represent a function

19). Graph does not represent a function

You newton, and Descartes volunteer this summer. You have 2 times as many volunteer min as newton Descartes have 5040 volunteer min altogether how many min do you volunteer

Answers

Complete question is;

You, newton, and Descartes volunteer this summer. You have 2 times as many volunteer min as newton and Descartes. You all have 5040 volunteer min altogether. how many min do you volunteer?

Answer:

2520 volunteer minutes

Step-by-step explanation:

You have 2 times as many volunteer minutes as Newton and Descartes.

Now, if Newton and Descartes each have x volunteer minutes, it means you have 2x volunteer minutes.

Since the total volunteer minutes of the 3 of you is 5040,then we have;

2x + x + x = 5040

4x = 5040

x = 5040/4

x = 1260

Since you have 2x volunteer minutes, then you have: 2 × 1260 = 2520 volunteer minutes

smash or pass? lets make this a trend :)

idea from dear amj1103

Answers

Answer:

Smash, all the Wayyyyyyyyyyyy

Answer:

Hehe

Step-by-step explanation:

EQUATIONS AND INEC
Worked examples
a) Solve these simultaneous equation by eliminating by subtraction.
5a + 2b = 16 equation 1
3a + 2b = 12 equation 2​

Answers

Answer:

a=2 and b=3

Step-by-step explanation:

5(2) +2(3) = 10 +6 =16

3(2) + 2(3) = 12

if
[tex]f(x) = \sqrt{x} + 12[/tex]
and
[tex]g(x) = 2 \sqrt{x} [/tex]
what is the value of
[tex](f - g)(144)[/tex]
?​

Answers

Answer:

0

Step-by-step explanation:

We have the two functions:

[tex]f(x)=\sqrt{x}+12\text{ and } g(x)=2\sqrt{x}[/tex]

And we want to find (f-g)(144).

This is the same thing to f(144)-g(144).

So, let’s determine the value of f(144) and g(144) first:

[tex]\begin{aligned} f(144)&=\sqrt{144}+12 \\ &=12+12 \\ &=24\end{aligned}[/tex]

And:

[tex]\begin{aligned} g(144)&=2\sqrt{144} \\ &=2(12) \\ &=24 \end{aligned}[/tex]

Hence:

[tex]\begin{aligned} (f-g)(144) &= f(144)-g(144) \\ &=24-24 \\ &=0 \end{aligned}[/tex]

Our final answer is 0.

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[tex](f - g)(x) = \sqrt{x} + 12 - 2 \sqrt{x} \\ [/tex]

[tex](f - g)(x) = - \sqrt{x} + 12[/tex]

[tex](f - g)(144) = - \sqrt{144} + 12[/tex]

[tex](f - g)(144) = - \sqrt{ {12}^{2} } + 12 [/tex]

[tex](f - g)(144) = - (12) + 12[/tex]

[tex](f - g)(144) = - 12 + 12[/tex]

[tex](f - g)(144) = 0[/tex]

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No entendi lpM explicen

Answers

no able engles? Don’t know if i spelt that right but

$330 is 12% less than the cost last year. Calculate the cost last year.

Answers

Answer:

just look that up and walla insta answer

The answer is $375! 12% of $375 is $45, and 330+45 is 375.

If you go on this question at all you are a republican and that is good

Answers

Answer: hahshejehdbddndb

Step-by-step explanation:

Answer:

you chose poison thanks for the points payback

Step-by-step explanation:

don't do this to people

its rude and people actualy need help not free points

Is there a constant rate of change? If yes, what is the rate?


Plz help I’m lost

Answers

What’s the question lol

2 = 2(m − 8) − 2
m =

Answers

Use distributive property
2 = 2m - 16 - 2
Simplify
2 = 2m - 18
Add 18
20 = 2m
m = 10
2 = 2m - 16 - 2
-16 - 2 = -18
2 = 2m - 18
2 = 20 - 18
m = 10

Megan's bank account is charged $9.95 per month for an online newspaper subscription how can you represent a change in her account balance after three months of charges

Answers

Answer:

T = C - (9.95 * 3)

Step-by-step explanation:

The account balance total can be calculated with the following equation where the variable T represents the final balance while the variable C represents her current balance before the three months...

T = C - (9.95 * 3)

The monthly charge is multiplied by the three months that Megan will be charged and then discounted from her current balance in order to give the new Total Balance after paying the subscription for the three months.

Karsyn is getting ready for her date. She has 20 outfits to choose from. Half of her
clothes are dirty. Her mom washed 3 more outfits, how many outfits would Karsyn have
had to choose from if she did her laundry?

Identify the variable:

Write the equation:

How many outfits did she have?

Answers

Well if she has 20 outfits and half of them are dirty then it’d be 10. This is because 20/2=10 but then if her mom washed 3 then it’d be 13. 10+3=13

The Allied Taxi Company charges $2.50 to pick up a passenger and then adds $1.95 per mile. Isaac was charged $27.46 to go from one city to another. If x represents the
BIG POINTS IF YOU ANSWER CORRECTLY PLEASE ANSWER ASAP number of miles driven by the taxi, which linear equation can be used to solve this problem, and how many miles did Isaac travel, rounded to the nearest tenth?

1.95x + 2.50 = 27.46; Isaac traveled 15.4 miles.
1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.
2.50x + 1.95 = 27.46; Isaac traveled 11.8 miles.
2.50x + 1.95 = 27.46; Isaac traveled 10.2 miles.

Answers

Answer:

It should be the second one

Step-by-step explanation:

Answer:

The answer is - 1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.

Step-by-step explanation:

Pls answer these and show work plss

Answers

Answer:

25x

Step-by-step explanation:

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