Mathematics, 30.07.2020 09:01 arrazolokhaliapb8sc2

A parabola, with its vertex at the origin, has a directrix at y = 3. Which statements about the parabola are true? Select two options. The focus is located at (0,–3).
The parabola opens to the left.
The p value can be determined by computing 4(3).
The parabola can be represented by the equation x2 = –12y.
The parabola can be represented by the equation y2 = 12x.

Answers: 3

Show answers

Answers

Answer from: arodavoarodavo

Using concepts from the equation of a parabola, it is found that:

The focus is located at (0,–3).The parabola can be represented by the equation x2 = –12y.

--------------------------------------

Equation of a parabola:

The equation of a parabola is given by:

(x - h)^2 = 4p(y - k)

The vertex is (h,k).The focus is at (h,k+p).The directrix is y = k - p.

--------------------------------------

Vertex at the origin means that h = 0, k = 0

.Directrix at y = 3 means that p = -3

.Directrix at the y-axis means the parabola opens upwards.Thus, the focus is: (0, 0 - 3) = (0,-3)

The p-value is: 4(-3) = -12.The equation of the parabola is:

x^2 = -12y

--------------------------------------

The correct options are:

The focus is located at (0,–3).The parabola can be represented by the equation x2 = –12y.

A similar problem is given at link

Answer from: my1445

Step-by-step explanation:

Let's answer these questions in an all-encompassing kind of explanation. If you plot the vertex and the directrix, you see that the vertex is below the directrix. Because of the fact that a parabola opens AWAY from the directrix, and wraps itself around the focus, we know it's an upside down parabola of the form

4p(y-k)=-(x-h)^2

The p value from the equation is a distance, specifically the distance between either the vertex and the directrix, or the vertex and the focus. The vertex is exactly in the middle of the directrix and the focus. So that tells us that the focus is 3 units below the vertex (because the directrix is 3 units above the vertex). We also know from this that p = 3.

Filling in the equation with a vertex of (0, 0) which is our h and k respectively:

4(3)(y-0)=-(x-0)^2 which simplifies to

12y=-x^2 and multiplying both sides by -1:

-12y=x^2 . This is not standard form, but it matches what your equation is in the choices. So to sum up:

The focus is located at (0, -3) and the first choice is true.

The parabola opens upside down and the second choice is not true.

The p value is found by counting the units between the vertex and the directrix, so the third choice is not true.

We solved the equation by filling in the values for h, k, and p and got that the equation in the fourth choice is true.

So the fifth choice is not true.

Answer from: Quest

21 is the answer the answer is 21

Answer from: Quest

answer: need picture of problem

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 14:30

In each bouquet of flowers, there are 2 roses and 3 white carnations. complete the table to find how many roses and carnations there are in 2 bouquets of flowers.

Answers: 1

Answer

Mathematics, 21.06.2019 15:30

Each of the four sides of a swimming pool measures 9 meters. the pool is 5 meters deep. how much water will be needed to fill it completely? a. 45 cubic meters b. 81 cubic meters c. 225 cubic meters d. 405 cubic meters reset next

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

Pat listed all the numbers that have 15 as a multiple write the numbers in pats list

Answers: 3

Answer

Mathematics, 21.06.2019 18:30

Which equation represents the model shown? a)1/3 divide 1/6 = 2 b)2/3 divide 1/6 = 2/18 c)1/3 divide 1/6 = 1/18 d)2/3 divide 1/6 =4

Answers: 1

Answer

You know the right answer?

A parabola, with its vertex at the origin, has a directrix at y = 3. Which statements about the para...