Function g can be thought of as a translated (shifted) version of f(x)=x^2 Write the equation for g(x),

Answers

Answer 1

Answer:

g(x) = (x - a)²     or

g(x) = (x + a)²    or

g(x) = x² + a      or

g(x) = (x + b)² + a      or

g(x) = (x + b)² - a      or

g(x) = (x - b)² + a      or

g(x) = (x - b)² - a

Step-by-step explanation:

Given equation:

f(x) = x²

This is the equation of a parabola with turning points at (0,0) facing up.

Now;

g(x) which is a shifted version of f(x) will have one of many forms depending on the nature of translation.

If f(x) = x² is shifted to the right by a units, then;

g(x) = (x - a)²

If f(x) = x² is shifted to the left by a units, then;

g(x) = (x + a)²

If f(x) = x² is shifted upwards by a units, then;

g(x) = x² + a

If f(x) = x² is shifted downwards by a units, then;

g(x) = x² - a

If f(x) = x² is shifted upwards by a units and to the left by b units, then;

g(x) = (x + b)² + a

If f(x) = x² is shifted downwards by a units and to the left by b units, then;

g(x) = (x + b)² - a

If f(x) = x² is shifted upwards by a units and to the right by b units, then;

g(x) = (x - b)² + a

If f(x) = x² is shifted downwards by a units and to the right by b units, then;

g(x) = (x - b)² - a


Related Questions

Look at this shape:
Which image shows a translation?

Answers

Answer:

The option C

Step-by-step explanation:

In the option A and B the image is been showed in either up-side down or mirror image. Only the option C has the image in a correct way and just moved the shape in a different position

The solution is Option C.

The image which shows a translation is Figure C.

What is Translation?

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the figure be represented as F

Now , the figure is translated up , down, or from side to side

The size of the figure does not change on translation

a)

The figure A has been inverted and it is not a transformation of translation

So , the Figure A is false

b)

The Figure B has been reflected by a factor , and reflection changes the coordinates of the figure F

So , Figure F is False

c)

The Figure C is translated by a factor of x to the left and y to downwards

The size of the figure remains the same

So , Figure C is a translation of Figure F

Hence , the figure C is a translation

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The cost a dog walker for n hours is given by f(n) = 5 + 10n. Which statement is true?

A. For each additional hour of service, the price of the dog walker increases by $15.
B. For each additional hour of service, the price of the dog walker increases by $5.
C. For each additional hour of service, the price of the dog walker increases by $10.
D. For each additional hour of service, the price of the dog walker decreases by $10.

Answers

Answer:

C. For each additional hour of service, the price of the dog walker increases by $10.

Step-by-step explanation:

Hope this helps!

:)

how much paper is needed to cover a rectangular bulliten board that is 29 in. wide and 37 in. high?

Answers

Answer:

1073 inches squared.

Step-by-step explanation:

To find how much paper is needed to cover the board, you have to find the area. The formula of area for rectangles is length times width or as you said in the question width times height.

To find the answer:

Area = length * width

Area = 29 * 37

Area = 1073 inches squared.

Don't forget to add the units!

The following two-way table shows the number of students of a school who have a cell phone and/or have a part-time job: Have Cell Phone Do Not Have Cell Phone Total Have Part time Job 40 10 50 Do Not Have Part time Job 10 40 50 Total 50 50 100 Based on the table, how many students have both a cell phone and a part-time job? (5 points) Question 14 options: 1) 10 2) 40 3) 50 4) 100

Answers

Answer:

I think it is B, so the correct answer is 40

Step-by-step explanation:

Answer:

The other guy is correct, the correct answer is B. 40.

Step-by-step explanation:

Under Students that have a cell phone and under students that have a part-time job the total amount of people is 40

HELPPPP!!!!



PLZZZZ!!

Answers

Answer:

the 2nd option is true

Step-by-step explanation:

slope for W = 1/2

slope for Z = 1/4

y-intercept for W = -1

y-intercept for Z = -2

y-value when w = -4 is 3 for both W and Z

Michelle drives her car around a square track each side of the track is 30 feet long. How many times does the car need to go around the track to go a total distance of1,200 feet/

Answers

Answer:

10 times

Step-by-step explanation:

distance covered once is equal to the perimeter of the square

perimeter of the square = 4 x length

4 x 30 = 120 ft

number of times = 1200 / 120 = 1-

Please help!! Thanks in advance!! NO links!!

Kallan will spin each spinner one time. What is the probability that the first spinner will land on a number greater than 7 and the second spinner will land on blue?

Answers

Answer:

probability for numbers greater than seven would be: 5/12

probability for landing on blue would be: 2/8

Step-by-step explanation

first, I counted all of the spaces, then I counted only the blue , or only the numbers over 7.

Help! Will give out brainliest

Answers

Answer:

75

Step-by-step explanation:

don't know how to explain hope this helps

it would be 75

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

Find the circumference

Answers

Answer:

c=pi*D

d=7

pi times 7= 21.98 is the circumference

c=pi*D

d=8

pi times 8=25.12 is the circumference

Step-by-step explanation:

5 balloons in 12 minutes. At this rate, how many balloons can she blow up in 3 hours?

Answers

Answer:

75 ballons in 3 hours

Step-by-step explanation:

We know the ratio min to balloon, 12:5.

A common factor of 60 is 12 and 5. We know that 5 balloons will come out of the 12 interval mark. [tex]5*5:12*5[/tex] So each hour, we get 25 balloons per hour. Multiply 3 on both sides of the equation to get the total amount of balloons. [tex]5*5*3:12*5*3[/tex]

So, 75 balloons is how many she can blow up in 3 hours.

Oliver purchased 11.3 gallons of gasoline. There are approximately 3.8 liters
in 1 gallon. Which measurement is closest to the number of liters of gasoline
Oliver purchased?
E) 40.84
F) 7.5L
G) 15.1 L
H) 42.94 L

Answers

Answer:b

Step-by-step explanation:

A triangle has interior angles of 101 degrees, 65 degrees, what is the other degree?

Answers

Answer:

180 degrees - 101 degrees - 65 degrees = 14 degrees

Plz answer this quick!!!

Answers

Answer:

3 Beings

Step-by-step explanation:

If 20% of them preferred quect juice and 15 were surveyed, then 3 preferred quect juice because 20% of 15 is 3!

Hope this helps! :)

The units of area and volume are..

Answers

Answer:

Area is measured in square kilometres

Step-by-step explanation:

Volume measures the space inside a 3-dimensional objects

PLEASE HELPP :(

Does the relationship shown in the table represent a direct or inverse variation relationship?

A: Direct, as x increases, y also increases
B: Direct, as x increases, y decreases
C: Inverse, as x increases, y also increases
D: Inverse, as x increases, y decreases ​

Answers

Step-by-step explanation:

i think

C: Inverse, as x increases, y also increases

Step-by-step explanation:

C: Inverse, as x increases, y also increases

hope it is helpful to you

‼️‼️‼️‼️can someone pls explain and what’s the answer? pls:)‼️‼️‼️‼️‼️‼️

Answers

4. would be B because the y column is being multiplied by 1.5

Answer:

4. B

(I'm not positive on what the answer to 5 is, so I won't guess bc I don't want u to get it wrong.)

Step-by-step explanation:

I know that the answer for 4 is B and I'll tell u why. B reads y = 1.5x

This means that when u multiply any number in the row marked "x" by 1.5 it should get the number that's right below it (in the "y" row).

This may sound confusing so let's add some context to it. When we chose the number 20 in the "x" row and multiply it by 1.5 the number we should get has to be 30 bc it's right below 20. In this case it IS so it is a true statement. Make sure to check the statement using different numbers from the row marked "x". (I already checked for u, but it's still a good tip to have )

HOWEVER, when we do a statement that does not correspond to the table

it will not give u a number that's below the row "x". If we use statement A, x = 1.5y that would mean that every number in row "y" should be the number on top of it (row "x") when multiplied by 1.5. This is a false statement bc 60 × 1.5 does not equal 40. If we keep trying with this statement, we will see that it's false. THE EQUATION THAT REPRESENTS THE DATA IN THE TABLE IS B.

29
7. Find the least number that must be added to 1300 so as to get a perfect square. Also, find the square root of the
perfect square​

Answers

Answer:

69 need to be added

Step-by-step explanation:

1300 +69 = 1369

37 ²  = 1,369

square root of 1,369 is 37

6(2x-3) - 2(2x+1)
can someone get an answer for that ASAP pls
no links :)​

Answers

Answer: 8x−20

Step-by-step explanation:

Distribute:

=(6)(2x)+(6)(−3)+(−2)(2x)+(−2)(1)

=12x+−18+−4x+−2

Combine Like Terms:

=12x+−18+−4x+−2

=(12x+−4x)+(−18+−2)

=8x+−20

Answer:

[tex]6 \times 2x = 12x\\ 6 \times - 3 = - 18 \\ - 2 \times 2x = 4x \\ - 2 \times 1 = - 2 \\ now \: add \: like \: terms \\ 12x - 4x = 8x \\ - 18 - 2 = 20 \\ \frac{ - 8x}{8} = \frac{20}{8} \\ x = 2.5 \: or \: \frac{5}{2} [/tex]

Step-by-step explanation:

brainiest please

pleas helppp!! lol :)

Answers

Answer:

Circumference of the circle with a radius of 5 is 31.42

Step-by-step explanation:

Answer:

The 1st one is: 31.4cm

Step-by-step explanation:

1st: 2 x 3.14 x 5 = 31.4

Here is the Math problem.

Answers

Answer:

Workup in photo below.

Step-by-step explanation:

Good luck.

BRAINLIEST IF UR CORRECT What is the correct answer?

Answers

Step-by-step explanation:

The function should look like this:

g(x) = 10^(x - 1) + 2

Select the correct answer.
What is the value of x in the triangle?

Answers

Answer:

D. 2√2

Step-by-step explanation:

sin 45° = 1/√2

P/H = 1/√2

x/4 = 1/√2

= 1/√2 × 4

= 4/√2

x = 4×√2/√2×√2

= 4√2 /2

= 2√2

Option D. 2√2

Which of the following is a true biconditional statement?
O
A. I walk one mile to the store if and only if the store is 5280 feet
away.
B. A person practices yoga if and only the person is relaxed.
c. I wear my raincoat if and only if it is raining.
D. An athlete wears a hat if and only if the athlete is on a baseball
team.

Answers

Answer:

C. I wear my raincoat if and only if it's raining

The length of rectangle PQRS is expressed as 2x+7. The width of rectangle PQRS is expressed as 3x−4. Which expression describes the area of rectangle PQRS?
A.6x^2
B.6x^2-29x-28
C.6x^2-15
D.6x^2+13x-28

Answers

Answer:

[tex]area = length \times width \\ = (2x + 7)(3x - 4) \\ = (6 {x}^{2} - 8x + 21x - 28) \\ = (6 {x}^{2} + 13x - 28) \: sq \: units[/tex]

The area of the rectangle PQRS is given by the formula D) 6x²+13x-28.

What is algebraic Expression?

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

The area of a rectangle is given by the formula:

A = l × w, where l is the length and w is the width.

In this case,

The length is 2x + 7 and the width is 3x - 4.

Therefore, the area of the rectangle is:

[tex]A = (2x + 7)(3x - 4)\\A = 6x^2 - 8x + 21x - 28\\A = 6x^2 + 13x - 28[/tex]

Therefore, the expression that describes the area of rectangle PQRS is D) 6x²+13x-28.

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For the quadratic y = x^2 -7x +12, when x = -3, what is the y-value?

Answers

Answer:

y = 0

Step-by-step explanation:

subsitute x = -3 into y = x^2 - 7x + 12

y = -3^2 - 7 x  -3 + 12

  = 9 - 21 + 12

  =  0

Answer: 42

Step-by-step explanation:

y= (-3)^2 -7(-3) +12

= (9) -(-21) +12

= 9+21+12

= 42

Please help!! Someone answered this already as a joke, I seriously need help on this

Answers

Question :-

Match the shape with the correct formula for finding the volume :-

SHAPES :-

ConeCylinder Triangular PrismRectangular Prism Pyramid

FORMULAE :-

[tex] \sf lwh[/tex] [tex] \sf Bh[/tex] [tex] \sf \frac{1}{3} \pi {r}^{2} h[/tex] [tex] \sf \pi {r}^{2} h[/tex] [tex] \sf \frac{1}{3} Bh[/tex]

____________________

Solution :-

Given Information :-

Shapes Formulae to calculate Volume

To Do :-

Match the shape with the correct formula for finding the volume.

Calculation :-

Cone = [tex] \sf \frac{1}{3} \pi {r}^{2} h[/tex] Cylinder = [tex] \sf \pi {r}^{2} h[/tex] Triangular Prism = [tex] \sf Bh[/tex] Rectangular Prism = [tex] \sf lwh[/tex] Pyramid = [tex] \sf \frac{1}{3} Bh[/tex]

____________________

Final Answers :-

Cone = [tex] \sf \frac{1}{3} \pi {r}^{2} h[/tex] Cylinder = [tex] \sf \pi {r}^{2} h[/tex] Triangular Prism = [tex] \sf Bh[/tex] Rectangular Prism = [tex] \sf lwh[/tex] Pyramid = [tex] \sf \frac{1}{3} Bh[/tex]

____________________

the cost to rent a paddleboat at the city park includes an initial fee of $7.00, plus $3.50 per hour. Which equation models the relationship between the total cost, Y, and the number of hours, X, that the paddleboat is rented?

A. y =3.5x+7 B. y =7x+3.5
B. y =7x+3.5
C. y =x/7+3.5 D. y =x/3.57
D. y =x/3.5+7

Answers

Answer:

the correct answer is A, y=3.5x + 7

HELP MEEEeeeeeEEEEEEEEEEE

Answers

Answer:

it's neptune hun

Step-by-step explanation:

Answer:

Neptune

Step-by-step explanation:

Like Jupiter and Saturn, Neptune radiates more hear than it receives. ... The average temperature on Neptune is a brutally cold -373 degrees F. Triton, Neptune's largest satellite, has the coldest temperature measured in our solar system at -391 degrees F.

Find the surface area of this rectangular prism. 4cm,9cm.5cm

Answers

Answer:

18cm

Step-by-step explanation:

A boat leaves the dock and travels 7 miles due south, then 24 miles due west.

How far is the boat from the dock?

A. 625 mi
B. 31 mi
C. 17 mi
D. 25 mi

Answers

Answer:

D

Step-by-step explanation:

The boat is a distance of 25 miles far away from the dock. which is the correct would be an option (D).

What is the right triangle?

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

A boat leaves the dock and travels 7 miles due south, then 24 miles due west which is given in the question.

According to Pythagoras's theorem,

In a right-angled triangle, "the square of the hypotenuse is equal to the sum of the squares of the other two sides."

perpendicular²+base²=hypotenuse²

The hypotenuse = c

Here , perpendicular = 7 and base = 24

⇒ 24² + 7² = c²

⇒ 576 + 49 = c²

⇒ 625 = c²

⇒ c² = 625

⇒ c = 25

Therefore, the boat is a distance of 25 miles far away from the dock.

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