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
RoseWind [281]
3 years ago
11

What is the focus of the parabola? y=14x2−x−1 Enter your answer in the space.. ( ?,? )

Mathematics
2 answers:
dmitriy555 [2]3 years ago
5 0
This is a vertical parabola which opens upwards
we have the general formula
(x - h)^2 = 4p(y - k)   where p is the  y coordinate of the focus

y/14 = x^2 - x /14 - 1/14

add 1/14 to both sides

y/14 + 1 /14 = x^2 - x /14

now complete the square  

y/14 + 1/14 = x^2 - x/14  + 1/28^2

y/14 + 1/14 = (x - 1/28)^2

(x - 1/28)^2 = 1/14( y + 1)


comparing this with the general form:-
4p = 1/14
p =  1/56

so the focus is at (h,p) = (1/28, 1/56)

Helga [31]3 years ago
3 0

Answer:

The focus of the parabola is (\frac{1}{28},-1).

Step-by-step explanation:

The given equation is

y=14x^2-x-1

y=14(x^2-\frac{x}{14})-1

Add and subtract (\frac{-b}{2})^2 in the equation to find the vertex form of the parabola.

y=14(x^2-\frac{x}{14}+(\frac{1}{28})^2-(\frac{1}{28})^2)-1

y=14(x-\frac{1}{28})^2-\frac{1}{56}-1

y=14(x-\frac{1}{28})^2-\frac{57}{56}                ... (1)

The standard equation of parabola is

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

Where, (h,k+p) is focus.

It can be written as

y=\frac{1}{4p}(x-h)^2+k                               .... (2)

From (1) and (2), we get

h=\frac{1}{28},k=\frac{-57}{56},\frac{1}{4p}=14\Rightarrow p=\frac{1}{56}

k+p=\frac{-57}{56}+\frac{1}{56}=\frac{-56}{56}=-1

(h,k+p)=(\frac{1}{28},-1)

Therefore the focus of the parabola is (\frac{1}{28},-1).

You might be interested in
10
Margaret [11]

Answer:

y=3x+19.

Step-by-step explanation:

1) according to the condition the line 't' is parallel to the line 's', it means, the equation of the line 't' is: y=3x+C, where C - unknown number.

2) in order to calculate the 'C', it need to substitute the given coordinates into the equation of the line 't', then:

-2=3*(-7)+C, ⇒ C=19.

3) if C=19 and the equation of the line 't' was y=3x+C, then it is possible to make up the full required equation:

y=3x+19.

7 0
2 years ago
What is 35.99 as a mixed number in simplest form
svp [43]
<span>35.99 = 33 and 99/100</span>
6 0
2 years ago
Read 2 more answers
In a shortage caused by a hurricane gas prices rose 15% it is now $2.80/gallon what was the price before
mash [69]

2.80*.15=.42

2.80-.42= 2.38

the answer is $2.38 (this was the price before)

8 0
3 years ago
Write a recursive formula for an, the nth term of the sequence 3, -4, -11
yKpoI14uk [10]

Answer:

, 12, 48, 192...

a. Write a recursive formula for the nth term of the sequence

Ans: a(n+1) = 4*a(n)

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

b. Write a general formula for the nth term of the sequence

a(n) = 3*4^(n-1)

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

c. Calculate S10 for this sequence

Geometric sequence with a(1) = 3 and r = 4

----?

Step-by-step explanation:

8 0
2 years ago
How do you solve this
marusya05 [52]
Hope this helps! Good luck!

3 0
3 years ago
Other questions:
  • The roots of the function f(x) = x2 – 2x – 3 are shown. what is the missing number? x = –1 and x =
    7·2 answers
  • Jayden makes a 5-sided spinner, numbered from 1 to 5. He records the number of times he scores a 3 from different numbers of spi
    14·1 answer
  • A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm,
    11·2 answers
  • A trapezoid has an area of 95 square meters. If the bases are 7 meters and 12 meters what is the height of the trapezoid
    5·1 answer
  • A cone has a volume of 24 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?
    6·1 answer
  • Pls help me fast ASAP
    9·1 answer
  • Five times the sum of a number and 3 equals 9
    14·1 answer
  • How do you know if an equation represents a proportional relationship?
    11·1 answer
  • The five patterns are: circle, plus sign, wavy lines, empty box, and star. One hundred trials were conducted, and your very impr
    13·1 answer
  • What’s the equation for this graph
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!