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
ch4aika [34]
2 years ago
11

Graph the function: y=(x-1)^2+3. how is the graph a translation of f(x)=x^2?

Mathematics
1 answer:
defon2 years ago
3 0

The answers D: Translated up 3 unit(s) and translated to the right 1 unit(s)

You might be interested in
The graphs of the quadratic functions f(x) = 6 – 10x2 and g(x) = 8 – (x – 2)2 are provided below. Observe there are TWO lines si
natta225 [31]

Answer:

a) y = 7.74*x + 7.5

b)  y = 1.148*x + 6.036

Step-by-step explanation:

Given:

                                  f(x) = 6 - 10*x^2

                                  g(x) = 8 - (x-2)^2

Find:

(a) The line simultaneously tangent to both graphs having the LARGEST slope has equation

(b) The other line simultaneously tangent to both graphs has equation,

Solution:

- Find the derivatives of the two functions given:

                                f'(x) = -20*x

                                g'(x) = -2*(x-2)

- Since, the derivative of both function depends on the x coordinate. We will choose a point x_o which is common for both the functions f(x) and g(x). Point: ( x_o , g(x_o)) Hence,

                                g'(x_o) = -2*(x_o -2)

- Now compute the gradient of a line tangent to both graphs at point (x_o , g(x_o) ) on g(x) graph and point ( x , f(x) ) on function f(x):

                                m = (g(x_o) - f(x)) / (x_o - x)

                                m = (8 - (x_o-2)^2 - 6 + 10*x^2) / (x_o - x)

                                m = (8 - (x_o^2 - 4*x_o + 4) - 6 + 10*x^2)/(x_o - x)

                                m = ( 8 - x_o^2 + 4*x_o -4 -6 +10*x^2) /(x_o - x)

                                m = ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x)

- Now the gradient of the line computed from a point on each graph m must be equal to the derivatives computed earlier for each function:

                                m = f'(x) = g'(x_o)

- We will develop the first expression:

                                m = f'(x)

                                ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

Eq 1.                          (-2 - x_o^2 + 4*x_o + 10*x^2) = -20*x*x_o + 20*x^2

And,

                              m = g'(x_o)

                              ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

                              -2 - x_o^2 + 4*x_o + 10*x^2 = -2(x_o - 2)(x_o - x)

Eq 2                       -2 - x_o^2 + 4*x_o+ 10*x^2 = -2(x_o^2 - x_o*(x + 2) + 2*x)

- Now subtract the two equations (Eq 1 - Eq 2):

                              -20*x*x_o + 20*x^2 + 2*x_o^2 - 2*x_o*(x + 2) + 4*x = 0

                              -22*x*x_o + 20*x^2 + 2*x_o^2 - 4*x_o + 4*x = 0

- Form factors:       20*x^2 - 20*x*x_o - 2*x*x_o + 2*x_o^2 - 4*x_o + 4*x = 0

                              20*x*(x - x_o) - 2*x_o*(x - x_o) + 4*(x - x_o) = 0

                               (x - x_o)(20*x - 2*x_o + 4) = 0  

                               x = x_o   ,     x_o = 10x + 2    

- For x_o = 10x + 2  ,

                               (g(10*x + 2) - f(x))/(10*x + 2 - x) = -20*x

                                (8 - 100*x^2 - 6 + 10*x^2)/(9*x + 2) = -20*x

                                (-90*x^2 + 2) = -180*x^2 - 40*x

                                90*x^2 + 40*x + 2 = 0  

- Solve the quadratic equation above:

                                 x = -0.0574, -0.387      

- Largest slope is at x = -0.387 where equation of line is:

                                  y - 4.502 = -20*(-0.387)*(x + 0.387)

                                  y = 7.74*x + 7.5          

- Other tangent line:

                                  y - 5.97 = 1.148*(x + 0.0574)

                                  y = 1.148*x + 6.036

6 0
2 years ago
A principal is purchasing a pencil for each of her students. The pencils come in packages of 24. If there are 1,008 students, ho
ratelena [41]
42 packages.


1,008 divided by 24=42

Hope that helps! :)
5 0
2 years ago
Inventory was taken on Day 1, Day 2, Day 5, Day 6, and Day 7. Norris wants to know roughly what the inventory was on Day 3.
Dvinal [7]

He should evaluate the function f(x)=−1/3 x+4 for x=3  , Option D is the correct answer.

<h3>What in Interpolation ?</h3>

Interpolation is when the line of best fit is used to determine the value of a point that is within the range of plotted points.

It is given to find the value at Day 3 which lies in the range of the points used for plotting

The line for best fit is

f(x) = (-1/3)x +4

At x = 3

f(3) = (-1/3) * 3 +4

f(3) = -1+4 = 3

Therefore He should evaluate the function f(x)=−1/3 x+4 for x=3

Option D is the correct answer.

To know more about Interpolation

brainly.com/question/18768845

#SPJ1

3 0
2 years ago
Read 2 more answers
An 8 foot square floor is to be covered with square tiles measuring 8 inches on each side. If each tile costs 50 cents, how much
wariber [46]

9514 1404 393

Answer:

  (c) $72

Step-by-step explanation:

Each tile is 8/12 ft = 2/3 ft on a side. Then 8/(2/3) = 12 tiles will fit along each edge of the square area to be tiled. That is ...

  12 × 12 = 144

tiles will be needed to cover the area.

The cost of 144 tiles at $0.50 each is ...

  (144)($0.50) = $72.00

8 0
3 years ago
A store that sells skis boys them from a manufacturer at a wholesale price of $57. The
Over [174]

Answer:

50 = 2

Step-by-step explanation:

which by definition equates to 68+1

3 0
3 years ago
Other questions:
  • 8 meters in 10 seconds
    12·2 answers
  • Rezolvați + explicație plzzzz
    6·1 answer
  • When fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes.
    13·1 answer
  • Find the measure of angle X
    7·2 answers
  • Enter the values for the highlighted variables to
    11·1 answer
  • Sooo what about this 200+204-100x3+1
    5·2 answers
  • The equation of a circle is ​ (x−10)2+(y−8)2=256. What is the center of the circle? Enter your answer in the boxes.
    10·1 answer
  • A 29 foot ladder leans against a building so that the angle between the ground and the ladder is 77º. How
    9·1 answer
  • An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 260260 engin
    7·2 answers
  • 6
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!