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
mixas84 [53]
3 years ago
14

What is the equation of the quadratic graph with a focus of (5, −1) and a directrix of y = 1?

Mathematics
2 answers:
pav-90 [236]3 years ago
5 0
(x-h)^2=4p(y-k)
vertex is (h,k)
p is the distance from focus to vertex and distance from vertex to directix (vertex is in middle of directix and focus)
if p is positive, the parabola opens up and the focus is above the directix
if p is negative, the parabola opens down and the focus is below the directix
 
we see the directix is over the focus (1>-1) so the parabola opens down and p is negative
distance from (5,-1) to y=1 is 2 units
2/2=1
p=-1 since p is negative
1 up from (5,-1) is (5,0)
veretx is (5,0)
(x-5)^2=4(-1)(y-0)
(x-5)^2=-4y is the equation
Lemur [1.5K]3 years ago
4 0
The answer is <span>directrix is horizontal, so the parabola is vertical </span>
<span>focus lies below the directrix, so the parabola opens downwards. </span>

<span>General equation for down-opening parabola: </span>
<span> y = a(x-h)²+k </span>
<span>with </span>
<span> a<0 </span>
<span> vertex (h,k) </span>
<span> focal length p = 1/|4a| </span>
<span> focus (h,k-p) </span>
<span> directrix (h,k+p) </span>

<span>Apply your data and solve for h, k, and a. </span>
<span>vertex is halfway between focus and directrix: (3,3) </span>
<span>h = 3 </span>
<span>k = 3 </span>

<span>distance between focus and vertex is 2, so p = 2. </span>
<span>a = -1/(4p) = -⅛ </span>

<span>y = -⅛(x-3)²+3 </span>
You might be interested in
Application of Trigonometric Ratios:
Irina-Kira [14]

9514 1404 393

Answer:

  15.46 m

Step-by-step explanation:

Side ratios of a 30°-60°-90° triangle are 1 : √3 : 2. That is, the height of the tree above eye-height is √3 times the distance from the trunk. The top of the crown will be at a height of ...

  1.6 m + (8 m)√3 ≈ 15.46 m

5 0
3 years ago
What is the value of X
ASHA 777 [7]
The answer is 21, 21 is the value of x
6 0
3 years ago
Please answer it’s a timed test
Feliz [49]

Answer:

i may be wroung but it should be 90

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Hurry please !! It’s timed...
ollegr [7]
The links don’t work.
6 0
3 years ago
You and your friend collect football cards. You tell your friend that you have 3 times the number of cards he has. Your friend r
fiasKO [112]
Easy I guess ..
I ll try to help ..
Here we go ..
The cards you have is N
The cards he has is n
<span>you have 3 times the number of cards he has
This means N=3n
</span><span> you only have 80 more football cards then he does
This means N=n+80
But we already know that N=3n
So 3n=n+80
which is 2n=80
n=40
So your friend has only 40 cards and you have 3*40= 120 cards

Best luck

Wise</span>
4 0
3 years ago
Other questions:
  • Find the local extreme values of the function f(x, y) = xy - x2 - y2 - 3x - 3y + 12
    9·1 answer
  • 100 POINTS PLS HELP !!! A star becomes twice as bright every 10 years
    7·2 answers
  • Using the Low Score System,a boat’s worst finish is thrown out and the remaining scores are added.The boat with the lowest total
    9·1 answer
  • Write an equation of the line that passes through a pair of points: (2, 3), (4, -2)
    6·1 answer
  • 1.The mass of an object, usually measured in kilograms and grams is?
    11·2 answers
  • Given the equation, y=2x+5 evaluate when x=2.
    5·1 answer
  • PLEASE HELP THIS IS DUE IN 20 MINUTES
    14·1 answer
  • Describe the overall shape of this distribution. Explain your answer in complete sentences.
    13·1 answer
  • A line's y-intercept is –9, and its slope is 1/6 .What is its equation in slope-intercept form?
    6·1 answer
  • Paloma says 3/6 and 3/8 are equivalent because
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!