1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vera_Pavlovna [14]
2 years ago
6

A parabola can be drawn given a focus of

Mathematics
2 answers:
Alina [70]2 years ago
6 0

Answer:

  • vertex: (8, 1)
  • p-value: -2
  • opens downward

Step-by-step explanation:

The vertex of a parabola is halfway between the focus and the directrix. The p-value of the equation is half the distance from the focus to the directrix. The parabola opens around the focus, away from the directrix.

__

<h3>vertex</h3>

That is, the vertex will lie on the same vertical line, but have a y-coordinate that is the average of the y-values of the focus and directrix. Here, that means the y-value of the vertex is ...

  (directrix +focus)/2 = (3 +(-2))/2 = 1

The focus is on the vertical line x=8. The coordinates of the vertex are (8, 1).

__

<h3>p-value</h3>

The parameter "p" is part of the leading coefficient of the quadratic defining the parabola. It fits into the vertex-form equation as shown here:

  y=\dfrac{1}{4\mathbf{p}}(x-h)^2+k\qquad\text{vertex at $(h,k)$}

The value of p is the distance from the focus to the vertex. When the focus is below the vertex, as here, the value of p will be negative.

  p = (focus y-value) - (vertex y-value) = (-1) -1

  p = -2

__

<h3>opening</h3>

The focus lies "inside" the parabola, and the directrix lies "outside." The parabola "wraps around" the focus, away from the directrix. When the focus is below the directrix, the parabola opens downward. (The leading coefficient of the equation is negative, telling you the same thing.

_____

<em>Additional comment</em>

The parabola is the set of points equidistant from the focus and directrix. Thus it should come as no surprise that the vertex is equidistant from the focus and directrix. They lie on the same vertical line when the directrix is horizontal.

The <em>latus rectum</em> is the line segment parallel to the directrix, through the focus, with end points on the parabola. Its end points always lie on a line with slope ±1/2 through the vertex. This can help you find (or verify) the focus graphically.

Brilliant_brown [7]2 years ago
5 0

Answer:

If you sketch the directrix and the focus, the vertex is halfway between them. It would be (-8,-1)

The p value is the distance from the focus to the vertex and the distance between the vertex and the directrix (they are the same) p=3.

The direction of the focus from the vertex will show which way it opens. The one opens down.

Step-by-step explanation:

hehe

You might be interested in
Put 4y= -3x - 8 into slope intercept form.​
zhuklara [117]

Answer:

y = -3/4x -2

Step-by-step explanation:

Slope intercept is y = mx+b where m is the slope and b is the y intercept

4y = -3x-8

Divide each side by 4

4y/4 = -3x/4 -8/4

y = -3/4x -2

8 0
2 years ago
What fraction is equal to 66?
marysya [2.9K]
The fraction equal to .66 is <span>33⁄50</span> 

 
5 0
3 years ago
Read 2 more answers
I need help please ASAP
azamat

What is the question

7 0
3 years ago
Read 2 more answers
8h=28 how do you solve this
Rashid [163]

Answer:

h=3.5

Step-by-step explanation:

divide 28 by 8

hope I helped

5 0
3 years ago
Read 2 more answers
What is the answer to 24=2k
Ilya [14]
Well, as you can see the answer and problem are switched so u do this

24=2k
÷2 ÷2
----------------------
12=k. check:

12×2 is 24☆

happy to help.

8 0
3 years ago
Other questions:
  • What is the mode of this data set<br> 8, 11, 20, 10
    13·1 answer
  • Wright an Expression to represent: three minus the product of two and a number z
    6·1 answer
  • Please help me with #75. Thanks
    6·1 answer
  • Please help! picture above plus, part B: write the quadratic expression in the numerator and the dominator in factored form. Par
    5·2 answers
  • A recipe calls for 1080 mL of broth. How many cups is that? (give answer in fraction form)
    11·1 answer
  • What is highest common factor of 98 and 42​
    8·2 answers
  • Please help me asap!!
    11·2 answers
  • a computer sales associate makes $74 each day that he works and makes approximately $20 in commission for each computer that he
    8·1 answer
  • Damian wrote the number nine and sixty-four thousandths as 9.64. Complete the
    7·1 answer
  • Find the slope below 4,1 4,-4
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!