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

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

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.

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:

[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

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

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


Plz help I’m lost

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.

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

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

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​?

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.

smash or pass? lets make this a trend :)

idea from dear amj1103

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, …

সৌরজগতের গ্রহ গুলোর চিএসহ বননা দাও​

No entendi lpM explicen

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.

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

Determine whether the graph represents 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

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)]

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

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

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?

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.

2 = 2(m − 8) − 2
m =

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.

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:

Pls answer these and show work plss

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]
?​

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

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

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?

I think of a number i halve it then subtract four

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