The parent function f(x) = x^2 is vertically stretched by a scale factor of 2, translated 14 units right, and 6 units up. Which equation below represents the new equation? 1. G(x) = 2(x-14)^2 + 6 2. G(x) = 1/2 (x-14)^2 = 6 3. G(x) = 2(x-14)^2 - 6 4. G(x) = 2(x+14)^2 + 6

Answers

Answer 1

Answer:

[tex](1)\; G(x)=2(x-14)^2+6[/tex]

Step-by-step explanation:

Assuming, right and up are positive directions.

The given parent function, [tex]f(x)=x^2[/tex]

Let [tex]f_1(x)[/tex] be the function when the parent function is stretched by a scale factor of 2.

So, [tex]f_1(x)=2f(x)[/tex]

[tex]\Rightarrow f_1(x)=2x^2[/tex]

Let [tex]f_2(x)[/tex] be the function when [tex]f_1(x)[/tex] is translated [tex]14[/tex] units right.

So, [tex]f_2(x)=f_1(x-14)[/tex]

[tex]\Rightarrow f_2(x)=2(x-14)^2[/tex]

Again, let [tex]f_3(x)[/tex] be the function when [tex]f_2(x)[/tex] is translated 4 units up.

So, [tex]f_3(x)=f_2(x)+6[/tex]

[tex]\Rightarrow f_3(x)=2(x-14)^2+6[/tex]

So, the resulting function, [tex]f_3(x)=G(x)=2(x-14)^2+6[/tex].

Hence, option (1) is correct.


Related Questions

Factorize the given expression and divide them as directed.


[tex](m^{2} -5m +6) divided (m-2)[/tex]

Answers

Answer :

We have to find :

m² - 5m + 6 / (m - 2) = ?

First of all, we need to factorize

(m² - 5m + 6)

⭆ m² - 5m + 6

⭆ m² - (3 + 2)m + 6

⭆ m² - 3m - 2m + 6

⭆ m(m - 3) - 2(m - 3)

(m - 2) (m - 3)

★ Division :

➠ m² - 5m + 6 / (m - 2)

➠ (m - 2) (m - 3) / (m - 2)

(m - 3) [Final answer][tex].[/tex]

Hope It Helps!

HELP PLZZZZZZZZZ!!!!!!!!!!

Answers

I’m pretty sure it’s d

Answer:

C

Step-by-step explanation:

Interior means on the inside. C is the only angle that is inside the shape.

helppp

britney has already run 10 miles on her own, and she expects to run 3 miles during each track practice. how many track practices would it take for britney to run 40 miles

Answers

Answer:

It would take her 10 track practices to get up to 40 miles.

Step-by-step explanation:

It’s due today so I’d like some help please

Answers

Answer:

The answer is E since you'll be adding 3.844 to each other and the terms as well. But the answer is E again

Answer:

E. 7.688 × 10^8

5 points
1.Mary has been saving her weekly allowance for the past 20 weeks. She
started with $100 and now has $300. Which equation can be used to find
the amount of money Mary receives for her weekly allowance? (7.10 A)
O A. 100 = 300 + 20%
B. 300 - 100x = 20
C.300 = 100 + 20x
D. 300 = 100 – 20x

Answers

ima go with B my dude good luck

(-2) + 3 = ?
Your answer

Answers

Answer:

(-2)+3=1

negative two plus three =one

Solve for x.

x/2 = -5

x = 5/2
x = -5/2
x = -10

Answers

Answer:

x = -10

Step-by-step explanation:

x/2 = -5

Multiply each side by 2

x/2 * 2 = -5 *2

x = -10

A gardener has 8300 plants.he wants to plant these in such a way that the number of rows and the number of columns remain same.find the number of plants left out in this arrangement

Answers

Answer:

19

Step-by-step explanation:

[tex]\sqrt{8300} = 91.1043[/tex]

row x columns = total

91 x 91 = 8281 plants

8300 - 8281 = 19 plants left out of arrangement

HELP what is 0.8120^-2=y16

Answers

Answer:

1.6280

Step-by-step explanation:

. Move all terms not containing y y to the right side of the equation.

68 is the product of h and 4

Answers

Answer:

h = 17

Step-by-step explanation:

68 / 4 = 17

Product  = multiplication but since we didn't have h we divided

Brainiest would be noice!

High Hopes^^

Barry-

Answer:

I think you are trying to find h if so h=17

all you have to do is divide 68 and 4

Please I need this help?

Answers

Answer:

6.35

Step-by-step explanation:

can someone tell me how to solve translations please?

Answers

Step-by-step explanation:

Hey there!

Here; The coordinates are ; H(-4,-2), G(-5,3), F(-2,1)

The translation P(x,y) = P'(X+7,y)

Use same formula.

H(-4,-2) -------> P'(3,-2)

G(-5,3)-----------> G'(2,3)

F(-2,1)------------> F'(5,1)

Therefore, the answer is Option C.

Hope it helps..

How do I do this?

Give the algebraic expression for each of the following:
The sum of 20 and a number, m

Answers

Answer:

The sum of 20 and a number,m = 20+m

8x-4=2(4x-4). Does this equation have only 1 solution?

Answers

Answer:

No, it has infinitely many solutions.

Step-by-step explanation:

A rectangle that is 2" x 3" has been scaled by a factor of seven suppose you want to scale the copy back to its original size what scale factor should you use

Answers

Answer:

5

Step-by-step explanation:

What are the solution(s) of x2-4-0?

X=-4 or X-4
X=-2 or X= 2
X=2
X=4

Answers

Answer:

X = - 2 or X = 2

Step-by-step explanation:

*completing the square*

X^2 - 4 = 0

X^2 = 4

X = +-√4

x = +-2

x= -2, 2

*factoring*

X^2 - 4 = 0

(x-2)(x+2) = 0

|. |

x = 2, x = -2

________________________________

(x-2)(x+2) = x(x+2) - 2(x+2) = x^2 + 2x - 2x - 4 = x^2-4

there are no 43 people in the cafeteria what is the inequality ​

Answers

Answer:

Step-by-step explanation:

if you have the option, you can say

# of people ≠ 43

What is the Next three term of this sequence 1,-3,-7,-11
Please help me

Answers

Answer:

-15, -19, -23

Step-by-step explanation:

Simply subtract 4 from the terms

Answer:

15 is the answer

Step-by-step explanation:

The cost to purchase a song from iTunes is $1.29 per song. To purchase a song from
Napster, you must be a member. The Napster membership fee is $10. In addition, each
purchased song costs $1.19. How many songs must be purchased for the monthly price of
Napster to be the same as iTunes?

Answers

Answer:

It will take 100 purchased songs for iTunes and Napster to equal in price.

Step-by-step explanation:

iTunes: y=1.29x

Napster: y=1.19x+10

1.29x=1.19x+10

10=.10x

x=100

I wish I...................to him yesterday?

Answers

wut—??????????????.....l......

had told

we use past perfect tense for wishes

for more dowload grammerly and check

PLZ HELP!!!!!!! A sequence is defined by the recursive function f(n + 1) = f(n) – 2.

If f(1) = 10, what is f(3)?

1

6

8

30...

Answers

Answer:

[tex]f(n + 1) = f(n) - 2 \\ n = 1 - - - - f(1 + 1) =f(1) - 2 \: \: \: - - - > \: \: f(2) = 10 - 2 = 8 \\ f(2) = 8 \\ n = 2 - - - - f(2 + 1) = f(2) - 2 \: \: \: - - - > \: \: \: f(3) = 8 - 2 = 6 \\ so \: f(3) = 6 \\ and \: we \: are \: done.[/tex]

Frank liked to buy packs of baseball cards. On 3 different days, he bought 3 packs. On 3 other days, he bought 4 packs each day. After that he split his packs with his 2 brothers. How many packs will they each have? Choose the expression that best matches this situation. [(3 x 3) + (4 x 3)] ÷ 3 [(3 x 3) + (4 x 3)] - 3 (3 x 3) + [(4 x 3) ÷ 3] [(3 x 3) + (4 x 3) ÷ 3]

Answers

Answer:

[(3 x 3) + (4 x 3)] ÷ 3

Step-by-step explanation:

Choose the expression that best matches this situation.

[(3 x 3) + (4 x 3)] ÷ 3

[(3 x 3) + (4 x 3)] - 3

(3 x 3) + [(4 x 3) ÷ 3]

[(3 x 3) + (4 x 3) ÷ 3]

On 3 different days, he bought 3 packs

= 3 × 3

= 9 packs

On 3 other days, he bought 4 packs each day.

= 4 × 3

= 12 packs

After that he split his packs with his 2 brothers

= (9 + 12) / 3

= 21 / 3

= 7 packs each for him and his two brothers

Here is the expression:

[(3 x 3) + (4 x 3)] ÷ 3

= (9 + 12) ÷ 3

= 21 / 3

= 7 packs

I'm building my first gaming pc, got any tips.

Answers

Answer:

A good graphics card.

Step-by-step explanation:

Answer: Most games are cpu based so get a good cpu. Also, too much rgb is not good, you need to spend more on your power supply than your rgb.

Step-by-step explanation:

whats the product of 1.74 * 10^(6) and 2.55 * 10^(7)?

Answers

Answer:

use calculator duh

Step-by-step explanation:

Answer:

3.12*10^-9

Step-by-step explanation:

took the test

Please answer this...

Answers

Answer and Step-by-step explanation:

The equation would be y = 5x + 75

Now, plug in 1, 2, 6, and 12 for x (which represents the hours) and solve for y (which represents the price).

1 hour - $80

2 hours - $85

6 hours - $105

12 hours - $135

Jasmine drives every morning to her office that is 12 miles from her home.


If Jasmine's average driving speed is s mph, how many hours does it take her to drive from her home to the office?

Answers

Answer:

is it s/12

Step-by-step explanation:

write a equivalent expression for 12a+60

Answers

Answer: 12(a+5)

Step-by-step explanation: factor out 12 from the expression

ANSWER 12(a+5)

A smartphone device has a certain cost. A person gets this smartphone and signs up for a monthly wireless plan with a fixed base price plus a charge per GB of data used. Which is the Independent Variable in this scenario? A. The cost of the smartphone device. B. The charge per GB of data used. C. The number of GB data used. D. The total amount they pay for the new device and new phone plan in the first month. Need an answer fast! Due very soon! Don't understand!

Answers

Answer:

The independent variable is: "the cost of the smart phone"

Step-by-step explanation:

An independent variable is simply one that doesn't depend on other variables measured in the same sentence.

Now, in the question, we are told that the smart phone device has a fixed cost. This means that the cost doesn't depend on any other variable mentioned in the sentence.

Thus, the independent variable is: "the cost of the smart phone"

What is the slope of the line that contains the points (-3, 2) and (-3, 5)?

Answers

Answer:

The slope is Undefined

Step-by-step explanation:

Use the slope formula to find the slope  m .

Answer:

Slope = Undifine

Convert 10 quarts (qt) to cubic feet (ft^3)

Answers

Answer:

10 US liquid quarts is 0.334201 cubic feet.          

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