f(x)=x^2
g(x) = (x– 9)^2 +3
We can think of g as a translated (shifted) version of f.

F(x)=x^2g(x) = (x 9)^2 +3We Can Think Of G As A Translated (shifted) Version Of F.

Answers

Answer 1

Answer:

To get the function g, shift f up by 3 units and to the right by 9 units.

Step-by-step explanation:

The given functions are

[tex]f(x)=x^2[/tex]

[tex]g(x)=(x-9)^2+3[/tex]

If f(x) is a parent function, then g(x) can be written in the form of f(x) as

[tex]g(x)=f(x-9)+3[/tex]        ...(1)

The translation is defined as

[tex]g(x)=f(x+a)2+b[/tex]       ... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2), we get

[tex]a=-9,b=3[/tex]

It means, to get the function g, shift f up by 3 units and to the right by 9 units.

Answer 2

Answer:

To get the function g, shift f up by 3 units and to the right by 9 units.

Step-by-step explanation:


Related Questions

What function is graphed below? y = - 1 y = 3 x y = x - 3 y = x + 3

Answers

Answer:

im confuised which one is a?

Step-by-step explanation:

Answer: y = x/3 -1

Step-by-step explanation: I also had this question so I know what graph you're talking about, but next time put a graph.

Given the translation T(3, -1), translate the ordered pairs (-3, 6) and (9, -8).

Answers

Answer:

[tex](-3,6) \implies (0,5)\\(9,-8) \implies (6,-9)[/tex]

Step-by-step explanation:

The translation [tex]T_{(3,-1)}[/tex] shows that we need to add three units to the x-cordinates and -1 units to y-coordinates, as follows

[tex](-3,6) \implies (0,5)\\(9,-8) \implies (6,-9)[/tex]

Therefore, the image of the coordinates are

[tex](-3,6) \implies (0,5)\\(9,-8) \implies (6,-9)[/tex]

randy and sandy are brother and sister. Randy is three less than twice Sandy's age. Together, their ages equal twent-four. How old is Sandy?

Answers

Answer:

Sandy is 9 years old.

Step-by-step explanation:

R+S=24

R=2S-3

R=Randy, S=Sandy

Plug the value of R into the first equation.

2S-3+S=24

Now, simplify.

3S-3=24

Now, solve the equation for S. First add three to both sides.

3S=24+3=27

3S=27

Now divide both sides by 3.

S=9

Based on the information given, the age of Sandy will be 9 years.

The equation that can be used to solve the question will be:

R + S = 24 .... i

R = 2S - 3 ..... ii

Put equation ii into i

R + S = 24

2S - 3 + S = 24

3S = 24 + 3

3S = 27

S = 27/3

S = 9

Therefore, the age of Sandy will be 9 years.

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Find the volume of this problem

Answers

Answer:

Step-by-step explanation:

diameter = 6 in

r = 6/2 = 3 in

h = 11 in

Volume of cylinder = πr²h

                                = 3.14*3*3*11

                                = 310.86 in³

Jane works 3 times as fast as Eleanor. If they work together they can do a job in 21 minutes. How long does it take Eleanor to do the job by herself?

Answers

Answer:

1 hour and 24 min

Step-by-step explanation:

Jane does 3/4 job done in 21 min

Eleanor does 1/4 job done in 21 min

21*4=84

60+24

1 hour and 24 min

The work rate when they work together is much higher than when Eleanor

does the job herself.

It will take 84 minutes

Reasons:

Jane's work rate = 3 × Eleanor's work rate

The time it takes both Jane and Eleanor to do a job = 21 minutes

Required:

The time it would take Eleanor to do the job herself.

Solution:

Let x represent the portion of the job performed by Eleanor in the 21

minutes, we have;

The portion performed by Jane = 3 × x

Therefore;

The job done when they work together for 21 minutes = x + 3·x = 4·x

The time it takes Eleanor to do the job portion, x = 21 minutes

Therefore;

The time it will take Eleanor to do a job of 4·x = 4 × 21 minutes = 84 minutes

The time it would take Eleanor to do the job herself = 84 minutes

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Which equations are equivalent to -1/4{X}=12 Select all that apply.

Answers

Answer:

2nd, 3rd and the last one

Factor the perfect square trinomial x2 - 12x + 36.

Answers

Answer:

(x - 6)(x - 6)

Step-by-step explanation:

-6 + -6 = -12

-6 * -6 = 36

meaning -6 in in both

if you want to find x

x = 6

Answer:

6

Step-by-step explanation:

x2-12x+36=0

find a two numbers that add to -12 and multiply to 36

-6 and -6

(x-6)(x-6)=0

x-6=0     x-6=0

x=6         x=6


How many faces does the rectangular solid have?
8
2
6
4

Answers

Answer:

This rectangular solid has 6 faces.

Step-by-step explanation:

The four sides and the top and bottom equal 6 faces.

Answer:

the answer is 6

Step-by-step explanation:

just count them

(: Please answer both questions :)
First person gets 50 points!

Answers

Answer:

1. 1350

2.2700

Step-by-step explanation:

Which algebraic expression represents the phrase "four times a number"?
4 + c
C-4
4-0
4c

Answers

Answer:

4c

Step-by-step explanation:

it pretty much means 4*c

Answer:

= 4c

Step-by-step explanation:

4×(c) . I hope it helps

find the minimum maximum and domain and range of the functions
h(x) = -x² + 4x - 2​

Answers

Domain (-infinity,infinity)

Min(?

max(2,2)

please help me thanks

Answers

___________________________________

The right answer is of option C

so if we have to solve it then it will be:

5x+13x=180

or,18x=180

or,X=180/18

X=10

hope it helps

Good luck on your assignment

_______________________________

Answer:

C

Step-by-step explanation:

X is 10 so it is c

Hope this works

Using substitution to alive equation with two variables

Answers

Answer:

X=27

Step-by-step explanation:

-4•4= -16

Move -16 to the other side

3x=81

x=27

what point is located on the graph of any proportional relationship​

Answers

Answer:

At the end

Step-by-step explanation:

What is the solution to the equation? 5=2/5a

Answers

a = 12.5

2/5 = 0.4
5/0.4 = a

Please help!!! WILL MARK BRAINLIEST ANSWER!!! A medical researcher designs a study that will investigate the effects of a
new drug on lowering patient's cholesterol level. The researcher randomly
selects participants for two groups. One group is given the new drug and the other group is given a placebo. Any person, within driving distance of the hospital, is allowed to participate and will be given a monetary compensation. Each sample consists of 5 patients. Select all weaknesses in the design.

Answers

 b. more groups should have been

Answer:

C AND D

Step-by-step explanation:

A rectangular room is 2 times as long as it is wide, and its perimeter is 36 meters. Find the width of the room.

Answers

36x2=72 which is the width so 72x2=144 so I’m pretty sure the length is 144

The width of the room is equal to 6 m

What is the area of the rectangle?

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here: Perimeter=36 m

Let the length of the room be 2x and width of the room be x

Then we have (2x+x)=36

                             x=12

Thus length =12m & width=6 m

Hence, the width of the room is equal to 6 m

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#SPJ2

The sum of the numbers 120. The third number is 4 times the second. The first number is 6 less than the second. What are the numbers?

Answers

Answer:

First number: 15

Second number: 21

Third number: 84

Step-by-step explanation:

A certain pizza box holds a 14-inch diameter pizza. If the box is 2 inches high; what is its surface area?
2 in.
14 in.
2 in.
2 in.
14 in.
14 in.
528 in 2
504 in 2
196 in 2
392 in 2

Answers

Answer:

528 in²

Step-by-step explanation:

Look at the attached image to help layout all of the dimensions of the pizza box!

Let me know if you have any other questions and please rate my response and consider marking brainliest!!

Evaluate this expression.
3^-2 ANSWER ASAP PLEASE

Answers

Answer:

0.11111111111

Step-by-step explanation:

Answer:

1/9 or 0.1 repeating

Step-by-step explanation:

Start by doing the inverse of the square root of 2 (that is the negative sign)

The inverse of 3^-2 is 1/3^2

Therefore, your answer is 1/9.

Hope this helps!

what is 2 with an exponent of negative 2 equal to?

Answers

Answer:

So since we have 2^-2 We can do 1/2^2  = 0.25

So if you have y^-x = 1/y^x

Answer:

1/4

Step-by-step explanation:

negative exponent rule says a ⁻ⁿ = 1/ aⁿ so:

2⁻² =1/2² = 1/4

what is the value of x if abc is equilateral

Answers

Answer:

d

Step-by-step explanation:

Since the triangle is equilateral then the 3 sides are congruent.

Equate any pair of sides and solve for x

AC = BC , that is

10x - 5 = 6x + 3 ( subtract 6x from both sides )

4x - 5 = 3 ( add 5 to both sides )

4x = 8 ( divide both sides by 4 )

x = 2 → d

A correct option is an option (d).

The given sides are,

AB=7.5x

AC=10x-5

BC=6x+3

As we know in an equilateral triangle all sides are equal then,

AB=AC=BC

[tex]AB=AC\\7.5x=10x-5\\-10x+7.5x=-5\\-2.5x=-5\\x=\frac{5}{2.5} \\x=2[/tex]

So, the correct option is an option (d).

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When is g(x) = 0 for the function g(x) = 5⋅23x + 4?

Answers

Answer:

4

Step-by-step explanation:

g(x)=0

Plug in 0

5*23(0) + 4

5*(0) + 4

0 + 4

= 4

In the diagram below BD is parallel to AE, BE bisects angle ABD, angle E is 37 degrees, angle BFE = 117, what is angle C

Answers

Angle C is 26 degrees

The coordinate of point B is -6 and the coordinate of point E is 2.
Find the length of segment BE.​

Answers

Answer:

4

Step-by-step explanation:

just because i just took it

Which expression is equivalent to RootIndex 3 StartRoot x Superscript 5 Baseline y EndRoot?

x Superscript five-thirds Baseline y

s Superscript five-thirds Baseline y Superscript one-third

x Superscript three-fifths Baseline y

x Superscript three-fifths Baseline y cubed

Answers

Answer:

The correct option is B:

B) x superscript five-thirds Baseline y superscript one-third

Step-by-step explanation:

The expression can be written as:

[tex]\sqrt[3]{x^5y}[/tex]

We know that cube root can also be written as the power of 1/3, So

[tex]\sqrt[3]{x^5y} = (x^5y)^{1/3}[/tex]

Multiplying the power with both variables

[tex](x^5y)^{1/3} = x^{5\cdot1/3}\cdot y^{1\cdot1/3}[/tex]

Simplifying the equation to get final form

[tex]x^{5\cdot1/3}\cdot y^{1\cdot1/3} = x^{5/3}\cdot y^{1/3}[/tex]

As we can see that it is similar to the option B which is

B) x superscript five-thirds Baseline y superscript one- third

the correct option is B

The expression which is equivalent to RootIndex 3 StartRoot x Superscript 5 Baseline y EndRoot is;

x Superscript five-thirds Baseline y Superscript one-third

The expression can be written as;

[tex] \sqrt[3]\frac{{ {x}^{5} } }{y} [/tex]

In essence, Upon simplification; we have;

x⁵ ^(1/3) × y^(-1/3)

Therefore, we have;

x^(5/3) × y (-1/3)

The expression therefore becomes;

[tex] \frac{ {x}^{ \frac{5}{3} } }{ {y}^{ \frac{1}{3} } } [/tex]

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Lauren has 108 pieces of candy leftover from Halloween. She would like to distribute them evenly to the 9 kids on her block. Write an equation to show how many pieces of candy each kid will receive. Somebody please Help!

Answers

Answer:

108/9 = 12

Take the total amount of Candy (108) and divide it by the amount of people that will receive an equal amount (9). 108/9 = 12

pls help help me need help!! thank you!!

Answers

Answer: 55 feet of rope

Step-by-step explanation:

The absolute value of -30 is the distance 30 is away from 0, so |-30| = 30. And |25| = 25.

|-30| + |25| = 30 + 25 = 55

A toy store marks down every toy by 15% in June. How much does a toy cost during June?

Answers

Answer:

since the toy is marked down 15%,

you do p*.85  

to find the remaining cost

Step-by-step explanation:

x2+3x-4=0. Find a=, b=, and c=. thank you:)​

Answers

Answer:

a=1 b=3 c=-4

Step-by-step explanation:

using almighty formular

a=1 b=3 c= - 4

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