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
A watercooler contains 160 cups of water. During practice, each person on a team fills a
STALIN [3.7K]
Yes, because 3 1/3 times 45 equals 150 which leaves 10 cups left over:
8 0
2 years ago
If x equals 3 calculate the value of 2x squared plus x
Korolek [52]
2 × 3 = 6
6 squared = 36
36 + 3 = 39
Hope this helps!
6 0
2 years ago
Read 2 more answers
For each pair of shapes, decide whether or not Shape A is congruent to Shape B. Explain your reasoning.
WINSTONCH [101]
Shape A is congruent to Shape B because If you were to rotate one of the two and flip it the would like up and match.
5 0
3 years ago
suppose you write an equation that gives "a" as a function of "b". Which is the dependent variable and which is the independent
blondinia [14]
If im not wrong which i may not the
Dependent is A
Independent is B
4 0
3 years ago
Read 2 more answers
Need help please thank you
umka21 [38]
2 cakes - Theresa's and Joe's
Theresa's cake had 6 pieces after she cut it. (2 times the size of Joe's pieces)
Joe's cake had 12 pieces after he cut it. (1/2 the size of Theresa's pieces)

We know that 8/12ths of ONE cake were eaten and that Joe ate 2 of his pieces.
We want to know how many pieces Theresa ate of her cake. Keeping in mind that her pieces are equal to 2 of Joe's pieces we can solve this question. 

8/12 eaten total
if 2/12 by Joe
then 8-2 = 6, 6/12 by Theresa
(BUT: Theresa's pieces were twice the size of Joe's so we will divide by 2)
6/12 = 3/6

Answer: Theresa ate 3 pieces of her cake

7 0
3 years ago
Other questions:
  • Solve the system using subtitution<br> 3x + 2y = 23<br> 1/2x - 4 = y
    11·1 answer
  • X + 3y = 14<br><br>-5x + 6y = -28<br><br><br>Solve systems by substitution
    15·1 answer
  • PLZ HELP ME WITH MEH 7th GRADE MATH
    10·1 answer
  • A construction firm is building a skyscraper, and the height of the skyscraper in yards and feet after certain numbers of days i
    11·1 answer
  • The diameter of a sphere is 4 centimeters. Which represents the volume of the sphere?
    15·2 answers
  • X^5(1-x)^6<br> How to find the critical points
    7·2 answers
  • PLS HELP I don’t understand
    11·1 answer
  • A school allots £3000 to spend on a trip to the theatre. Theatre tickets have a regular cost of £40 each and are on offer for 1
    14·1 answer
  • The graph below shows the price of different numbers of swim bags at a store:
    6·2 answers
  • What is the range of this function?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!