A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (-4, -5)(−4,−5). What is the vertex of the function defined as g(x)=f(x+2)+3g(x)=f(x+2)+3?

Answers

Answer 1

Answer:

The vertex of the function g(x) = f(x + 2) + 3 is (-6, -2)

Step-by-step explanation:

If the graph of the function f(x) is translated h units to the left, then its image g(x) = f(x + h)If the graph of the function f(x) is translated k units up, then its image g(x) = f(x) + k

Let us use these facts above to solve the question

∵ The quadratic function f(x) = y has a vertex point (-4, -5)

g(x) = f(x + 2) + 3

→ By using the two facts above

∴ f(x) is translated 2 units to the left

∴ f(x) is translated 3 units up

→ That means the vertex point must move 2 units left and 3 units up

∵ The rule of translation is T (x, y) → (x - 2, y + 3)

∵ The coordinates of the vertex point of f(x) are (-4, -5)

∴ Its image is (-4 - 2, -5 + 3)

∴ Its image is (-6, -2)

The vertex of the function g(x) = f(x + 2) + 3 is (-6, -2)


Related Questions

What is an equation of the line that passes through the points (6, 4) and (4,1)?

Answers

Answer:

3/2 x-5

Step-by-step explanation:

Answer:

y=3/2x-5

Step-by-step explanation:

m=y²-y¹/x²-x¹

m=1-4/4-6

m=-3/-2

m3/2

y-y=m(x-x1)

y-1=3/2(x-4)

y-1=3/2x-6

+1 +1

y=3/2x-5

system of equations
3x+5y=-7

6x-4y=0​

Answers

Step-by-step explanation:

18x+30y=-7

18x+12y=0

42y=-7

y=-0.17

3x+5(-0.17)=-7

3x-0.85=-7

3x=-6.15

x=-2.05

8 coins are tossed simultaneously, find the chance of obtaining at least six heads​

Answers

Answer:

37/256

Step-by-step explanation:

We need to use the Binomial distribution here, ask me why?

because there are only two outcomes of the experiment, heads or tails, which are complementary by nature, that is to say they are mutually exclusive and if one doesn't happen the other definitely does

p(head)+p(tail) = 1

also the trials are independent of one another, that is to say that the outcome of one toss doesn't affect the outcome of any of the other seven tosses out of 8.

and I am assuming here that the coins are all unbiased, i.e. p(head)=p(tail)=0.50

Considering all of these the possibility that we will get at least 6 heads out of 8 tosses is given by

p(head=6)+p(head=7)+p(head=8)= 8C6 (0.5)^6 (0.5)^2 + 8C7 (0.5)^7 (0.5)^1 + 8C8 (0.5) ^8

The plus sign indicates OR operator, i.e. we might get 6 heads or 7 heads or 8 heads.

where the probability mass function of the bin distn is given by

nCx p^x q^(n-x)

n= total number of trials

x= no. of success (in our case no of heads)

n-x = no of failures (no of tails in this example)

p= probability of success (p(heads)=0.5)

q= probability of failure (is equivalent of 1-p)

Determine weather the following is real or complex
i^6-122-7i^2

Answers

Answer:

Real

Step-by-step explanation:

i^6-122-7i^2

(i^2)^3-122-7i^2

(-1)^3-122-7×(-1)

-1-122+7

-123+7

-116

So the final answer is -116

i just got done cutting and taking out the seeds of chilies and i went to go use the restroom and now my bottom part is BURNING HELP ME

Answers

Answer:

Lol I can't help im sorry

how do you find inital value on a graph I forgot how???????????????????????

Answers

Answer:

I believe you would look for what x is when y is 0, but I may be wrong.

the y intercept is the initial value

Write the hypothesis: If the pen is not blue then today is Friday.

a. The pen is not blue
b. If the pen is not blue
c. If today is Friday
d. today is not Friday

Answers

The answer is b. If the pen is not blue

A star patterned quilt has a star with the angels shown. What is the value of x? Explain your answer.

Answers

Answer:

81°

Step-by-step explanation:

x° and 24° are interior angles of a triangle that are opposite to an exterior angle of measure 105°. According to the exterior angle theorem of a triangle, thus:

[tex] x + 24 = 105 [/tex]

Subtract 24 from both sides

[tex] x + 24 - 24 = 105 - 24 [/tex]

[tex] x = 81 [/tex]

Value of x = 81°

WHATS A FUTURE FUNKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

500,325+6,773,500,135

Answers

Answer: future the time or a period of time following the moment of speaking or writing; time regarded as still to come.

Step-by-step explanation:

can u pls help me with this question ​

Answers

Answer:

A

Step-by-step explanation:

Options A, B and C  are the same:

2/3 is two-thirds (that how we read the fraction in English) and is 0.66666... (a decimal is sometimes permissible)

But most common and most used is a fraction

So, the answer is A

A carpenter needs to cut two pieces of trim around a window at 34 3/8 inches each. If the saw blade will remove 1/8 of an inch of wood, what is the smallest piece of wood that can be used to produce both pieces?

Answers

Answer:

It is so ez, it is of course 2

Step-by-step explanation:

Lilly was shopping and saw the following prices on different packages of the same item

Answers

Answer:

What's the question?

Step-by-step explanation:

In City​ A, 4,099 of 5,289 ​residents, have reliable​ high-speed internet access. In City​ B, 15,798 of 20,868 residents have reliable​ high-speed internet access. In which town are residents more likely to have reliable​ high-speed internet​ access?

Answers

Answer:

4,099 and 5,011

Step-by-step explanation:

The answer is 4,099 and 5,011

So far, a storm has traveled 35 miles in half an hour. If it is currently 5:00 pm and the storm is 105 miles away, what time will the storm reach you? Explain how you solved the problem.

Answers

Answer:

It will reach you at 6:30.

Step-by-step explanation:

THe storm traveled at 35 miles in half an hour. It is 105 miles away.

Divide 105 by 35 to get how many half hours it will take to rach you.

105 ÷ 35 = 3.

So, it will be 3 half hours or one hour and a half.

Add that time to the current time, which is 5:00.

It will be 6:30 when the storm reaches you.

hope this helped tell me if it is right.  

A card is drawn from a deck of 52 cards.
Find the probability of drawing a black 8:

Answers

Answer:

1/26

Step-by-step explanation:

There are two sets colors; red and black.

13 ranks, each rank has 2 black cards and 2 red

but there are only 2 black eights

2/52

Let x represent the price of a movie ticket. A local movie theater decided to increase the price of a movie ticket by 30%. Which expression can be used to calculate the new, increased price of a movie ticket?
A. 30x
B. x over the number 30
C. 0.3x
D. 1.3x

Answers

Answer:

A

Step-by-step explanation:

30 times x all the others are incorrect so by process of elimination it is a

Please help me I beg you I really need help.

Answers

Answer:

what's that ,we are all ears

What is the Magnitude of 6.8

Answers

        (っ◔◡◔)っ ♥ Hey Honey Here!♥Answer♥

Santiago Chile (AP)

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                                                   ♥ お力になれて、嬉しいです

Find the lengths of the sides of the triangle PQR. P(3, â3, â3), Q(9, 0, 3), R(12, â6, â3) |PQ| = |QR| = |RP| = Is it a right triangle?

a. Yes
b. No
c. Is it an isosceles triangle?

Answers

Answer:

a. Yes

Step-by-step explanation:

find the missing side lengths. leave ur answers as radicals

Answers

Because of the 45 45 90 theorem since the hypotenuse is 9√2 x and y are both 9

A cell phone tower and a fence are on the same property. the fence is 8 feet tall and has a shadow that measures 14.5 feet. the shadow of the cell phone tower measures 72.5 feet . how tall is the cell phone tower ?​

Answers

Answer:

40 feets

Step-by-step explanation:

Given that:

Height of fence = 8 feets

Shadow of fence = 14.5 feets

Shadow of cell phone tower = 72.5 feets

Height of cell phone tower = x

Height of fence = shadow of fence

Height of tower = shadow of tower

8 feets= 14.5 feets

x feets = 72.5

Cross multiply :

(14.5 * x) = (72.5 * 8)

14.5x = 580 feets

x = 580/14.5

x = 40 feets

Hence, the height of the cell phone tower is 40 feets

will give branlist

The sum of two numbers is 107, the difference is 51. Find the numbers.

Answers

Answer:

Answer is 79 and 28

Step-by-step explanation:

Let two numbers be x and y.

x + y = 107. --> 1

x - y = 51 -->2

solving above equations,

2x = 158

x =79

y = 28

Complete the equation that represents the total value of the nickels and p pennies

Answers

Answer:

Answers below

Step-by-step explanation:

Equation

Let's call:

p = number of pennies Janesa has in her pocket

n = number of nickels Janesa has in her pocket

She has 24 coins in total, thus:

[tex]p + n=24\qquad\qquad [1][/tex]

Since each penny is worth $0.01 and each nickel is worth $0.05, and Janesa has $1 in total:

[tex]0.01p+0.05n=1[/tex]

Multiplying by 100:

[tex]p+5n=100\qquad\qquad [2][/tex]

A. Completing the equation:

[tex]5n+p=100[/tex]

B.

From [1]:

[tex]p=24-n[/tex]

Substituting into [2]:

[tex]24-n+5n=100[/tex]

Simplifying:

[tex]24+4n=100[/tex]

Rearranging:

[tex]4n=100-24=76[/tex]

[tex]n=76 / 4= 19[/tex]

[tex]p=24-19=5[/tex]

B. There are 5 pennies in Janesa's pocket

C. Since each penny is worth $0.01, the total value of pennies is 5*$0.01=$0.05

The total value of the pennies is $0.05

D. The total value of the nickels is 19*$0.05 = $0.95

E. Jackson should say she has 19 nickels and 5 pennies

janesa has 24 coins in her pocket worth exactly $1.00. she tells her younger brother jackson that he can have the coins if he correctly guesses how many of each coin she has. she gives him the hint that there are only nickels and pennies. complete the equation that represents the total value of the nickels and p pennies 5( blank ) + p = 100 The type of coins that Janessa has = nickels and pennies.

Janessa has a total number of 24 coins

The sum of the nickels and pennies = $1.00

Let us represent the number of nickels as x

The number of pennies as y

What is the result when the number 63 is decreased by 1.3%?

Answers

Answer:

61.7

Step-by-step explanation:

How many ways can you arrange the word HOCKEY using only 5 letters
if each letter can only be used once?

Answers

Answer:

Total arrangement = 720

Step-by-step explanation:

Given:

Total letter n = 6

Using letter r = 5

Computation:

Total arrangement = nPr

Total arrangement = !n / !(n-r)

Total arrangement = !6 / !(6-5)

Total arrangement = 6 x 5 x 4 x 3 x 2

Total arrangement = 720

Identify the coefficient in 0.50(m)-0.20(g)+9.00

Answers

Answer:

-0.2 + 0.5m + 9

Step-by-step explanation: simplify

2) What is 75% of $20.00? *
A. 1,500
B. $15.00
C. $0.15
D. $150.00

Answers

The answer is B $15.00

Answer:

It is $15.00

Step-by-step explanation:

It is B because A is not even money, C is fifteen cents which is not correct because the question is asking for 75% of $20.00, and finally D is incorrect because it is more than the amount of money asked in the question.

HELPPPPP PLEASEEEEE!!!!!!!!!

Answers

The x intercept is (9/2,0) or (4.5,0). The y intercept is (0,-1):)

How did the National Woman Suffrage Association (NWSA) differ from the American Woman Suffrage Association (AWSA)?

Answers

Answer:

The National Woman Suffrage Association advocated for a range of reforms to make women equal members of society, such as the right to own property, etc. The American Woman Suffrage Association lobbied state governments to enact laws granting or expanding women's right to vote in the United States.

Answer:

C: The NWSA wanted to address the voting rights of both women and formerly enslaved people.

Step-by-step explanation:

The NWSA wanted to address and justify the rights of both former slaves and women, while the AWSA only wanted to either help women or former slaves, not simultaneously.

Which would be the best concluding sentence?
Tom wrote this paragraph:
Eating at Joe's Pizza Place is a delightful experience.
The food is freshly prepared right there in the
kitchen. Joe uses only the
freshest ingredients and
makes his own tomato sauce. He even makes
homemade sausage.
O Joe's wife, Emma, has decorated the restaurant
with great care.
O A mural on the wall shows Joe making his tomato
sauce at the Pizza Place.
O Joe also keeps a close eye on the servers and
makes sure customers are happy.
O Anyone who enjoys great food should plan a visit to
Joe's Pizza Place.
lol

Answers

the last one seems to be the best

Answer:

D

Step-by-step explanation:

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