A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is (6, -3). What is the vertex of the function defined as
g(x) = f(-x) - 3?

Answers

Answer 1

Answer: (-6, - 6)

Step-by-step explanation:

Here we have two transformations, and the first step will be to explain those transformations:

Reflection over the y-axis.

For a function f(x), the reflection over the y-axis is written as:

g(x) = f(-x)

Then if we initially had a point (x, y), the transformed point will be (-x, y).

Vertical translation.

We can define a vertical translation of N units as:

g(x) = f(x) + N

if N > 0, the translation is up.

If N < 0, the translation is down.

Then if we start with a point (x, y), the transformed point will be (x, y + N)

In the case of this problem we have g(x) = f(-x) - 3

This means that N = -3

Then if we initially had the vertex at the point (6, - 3)

The transformed point will be: changing the sign of the x-component and subtracting 3 in the y-component, then the transformed vertex point is:

(-6, -3 - 3) = (-6, - 6)

Answer 2

The vertex of the resulting  parabola will be (-6, -6)

Rule of reflection

Given the function y= f(x), plotted on a graph and the vertex of the resulting

parabola is (6, -3), if this coordinate is reflected over the y-axis, the reflection rule will be:

[tex](x,y) \rightarrow (-x, y)[/tex]The coordinate (6, -3) under this translation will give (-6, -3)

To get the corresponding function [tex]g(x) = f(x) - 3\\[/tex]

[tex]g(x) = [(-6, -3) - 3]\\g(x) = (-6, -3-3)\\g(x) =(-6, -6)[/tex]

Hence the vertex of the resulting  parabola will be (-6, -6)

Learn more on reflection here: https://brainly.com/question/14460986


Related Questions

I need all of these please

Answers

Answer:

Step-by-step explanation:

this is the solve for the first q. only sorry

I need help with this please.

Answers

Answer:

CCCC.

Step-by-step explanation:

Select the correct answer

Answers

Answer:

Option B

Step-by-step explanation:

Domain of a function is represented by the set input values or x-values

Range of the function is represented by the set of output values or y-values.

From the graph attached,

y-values are varying from y = - 9 to y = 8.

Therefore, range of the function from the given graph will be,

-9 ≤ y ≤ 8

Option B will be the correct option.

What is the 51st term of the arithmetic sequence 29,9,-11

Answers

Answer:

-951

Step-by-step explanation:

an=a1+(n−1)d

\begin{gathered}29 = a_1 + (1-1)d\\29 = a_1\\9 = 29 + (2-1)d\\9 = 29 + d\\d = -20\\a_n = 29 -20 (n-1)\\a_n = 29 - 20n+20\\a_n = -20n + 49\\\\a_51 = -20(51) + 49 = -951\end{gathered}29=a1+(1−1)d29=a19=29+(2−1)d9=29+dd=−20an=29−20(n−1)an=29−20n+20an=−20n+49a51=−20(51)+49=−951

The 51st term of the arithmetic sequence 29,9,-11 is -971 or a(51) = -971.

What is a sequence?

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

It is given that:

The sequence is:

29, 9, -11

The above sequence represents an arithmetic sequence:

The common difference d = 9 - 29

d = -20

The first term a = 29

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.

The nth term of the AP:

a(n) = a + (n-1)d

a(n) = 29 + (n - 1)[-20]

a(n) = 29 -20n +20

a(n) = 29 -20n +20

a(n) = 49 - 20n

Plug n = 51

a(51) = 49 - 20(51)

a(51) = -971

Thus, the 51st term of the arithmetic sequence 29,9,-11 is -971 or a(51) = -971.

Learn more about the sequence here:

brainly.com/question/21961097

#SPJ2

PLEASE HELPPPP
Find the equation of the linear function represented by the table below in slope-
intercept form.
X
O
1
2
3
4
y
6
14
22
30
38
Answer: y =
Submit Answer

Answers

Answer:

yo done so easy

Step-by-step explanation:

the answer is y=8x + 6

please help me solve

Answers

Answer:

CD

Step-by-step explanation:

Answer:

3rd one

Step-by-step explanation:

Total Cost of Computer Repair = $1,444.50

Shipping = 2 percent of Total Cost

If Sarah wanted to include a 15 percent gratuity, based on the total cost of the computer repair, excluding shipping, how would you find her new total cost?

Answers

Answer:

Its D

Step-by-step explanation:

0.02 ($1,444.50)

Answer:

D

Step-by-step explanation:

Enuncia 5 vectores que pertenecen a un mismo sub espacio

Answers

Answer:

what?

Step-by-step explanation:

Which is the best description for the graph?
O The graph is increasing everywhere.
O The graph is decreasing everywhere.
O The graph is increasing, then decreasing.
O The graph is decreasing, then increasing.

Answers

i think it’s the graph is decreasing everywhere
The graph is decreasing everywhere.

11) Select the best answer.

How many significant figures does the following number have?

0.056
4
5
3
2
1

Answers

There are 2 sig figs
it has 2 significant figures

I NEED HELP PLZ ITS FOR MY FINAL

Answers

Pls help me and explain why it’s that answers. Pls help me and explain why it’s that answers. Pls help me and explain why it’s that answers. Pls help me and explain why it’s that answers. Pls help me and explain why it’s that Pls help me and explain why it’s that answers. answers.

100 points! help please I need this

Answers

Answer:

5/4 is rational , 100 square root is irrational , 7.3 rational , 0.00247 is rational , 4/9 square root is irrational ,2/24 square root is irrational and 0.01 is rational :)

A and B are independent events.
PA) = 0.6
P(B) = 0.4
What is P(AB)?
O A. 0.24
B. 0.6
O c.0.4
D. Not enough information

Answers

Answer:

not enough information

Answer:

It's 0.6

Step-by-step explanation:

This symbol means that both sets could have the same elements. (A ⊆ B)
True
False

Answers

Answer:

true

Step-by-step explanation:

because it is

Answer:

True

Step-by-step explanation:

What is the y-intercept of the parabola defined by y=−2x2+6x−8 and what is the equation of the axis of symmetry?

Answers

Answer:

y-intercept = (0, 8)

axis of symmetry= -b/2a

Step-by-step explanation:

Also when you want something to be squared use this symbol ^

What of the following lines is perpendicular to the line passing across the points (1,1) and (-5,-6)?

y = 6/7x + 1

y = -6/7x + 1

y = -6/7x - 1

y = 6/7x - 1

Answers

First find slope
(-6-1)/(-5-1) = -7/-6 = 7/6
Perpendicular = opposite sign and reciprocal slope
Slope would be -6/7
It would be anything with slope of -6/7

Does this scatter plot show a positive trend, a negative trend, or no trend?​

Answers

it shows a negative trend

Answer:

no trend

a positive trend would start in the bottom left and go toward the top right

a negative trend would start at the top left and go town the bottom right

this is an example of no trend

Step-by-step explanation:

a "trend" shows an increasing or decreasing relationship between the x and y values, in this they don't have any sort of relationship. you can tell by the repeating y values for multiple different x-values, or the repeating x-values for multiple different y-values.

Find the coefficient of x^2 y^3 in the expansion of (-4x+y)^5. Give your answer as an integer.

Answers

Coefficients are the numbers in front of the variables therefore The coefficient of x^2 y^3 would be (-4)x and 1(y). Anytime there isn’t a coefficient shown in front of a variable the coefficient will always be 1. I hope this helped :)

Please give me the correct answer ​

Answers

Answer:

the first one; 3*1/10^-4

Step-by-step explanation:

10^-4 can be ocnverted into a fraction: 1/10^4

Answer:

3 times 1/10,000

Step-by-step explanation:

30 is 2/3 of what number

Answers

Answer:45

Step-by-step explanation:

Key Word:of

30*2/3 = 45

Answer:

Step-by-step explanation:

let the number be x.

then,

2/3 of x = 30

=> 2/3x = 30

=> x = 30 × 3/2

=> x = 45

so, the required number is 45 .

hope it helps...!!!

Solve the equation.
-5r-1=7r+5

Answers

Answer:

r=-1/2

Step-by-step explanation:

(-5*-1/2=2.5)( 2.5-1=1.5) (7x -1/2= -3.5)-3.5+5 =1.5

IF I GET AN ANSWER IN 10 MIN UR VOTED BRAINLIEST
whats the best way to remember whether a number is positive or negative when adding subtracting multiplying and dividing?

Answers

Adding and subtracting with negative numbers

First, recognize that adding and subtracting are, from one viewpoint, the same thing. Subtracting a number is the same thing as adding the negative of that number. For example, 4 – 12 is the same as 4 + –12 (which, because the order of terms doesn't matter with addition, is the same as –12 + 4). With that in mind, here are the rules for adding with negative and positive numbers:

If both numbers are positive, then the answer is positive.

If both numbers are negative, then the answer is negative.

If the numbers have different signs, the answer takes the sign of the higher number.

Subtracting a negative number is the same as adding the positive of that number. For example, 5 – –4 is the same as 5 + 4.

Multiplying and dividing with negative numbers if the numbers have different signs, the answer is negative.

A mail carrier travels at 15 miles per hour through a neighborhood. Which table
represents the distance the mail carrier travels in x hours?
2
G
H
0 1 3
yo 16 18
0 24
yo 30 55
x 135
y 15 45 75
x 134
y 15 40 55

Answers

Answer:

Step-by-step explanation:

the table is not copied correctly, I assume

the mail carrier will travel a distance of 15x

question is in the picture pls help me. much appreciated

Answers

Okay for a diagonal length it isn’t to hard. So 2y-3 is half of the 12 diagonal

So 2y-3+ 2y-3 = 12 or 4y-6= 12
Add 6 to both sides 4y=20
Divide 4 from both sides y=5

Hope this helps

Question is in the image​

Answers

Answer:

4.

Step-by-step explanation:

y = -2x + 3

-1 = -2(2) + 3

-1 = -4 + 3

-1 = -1

y = x - 3

-1 = 2 - 3

-1 = -1

Let g (2) = 22 – 5 and h (2) = 22 +1.
Find (g+h) (2)

Answers

Answer:

23 + 17 = 40 :)

Solve – 4y – 10 = 4(y - 3)

Answers

Answer:

y= 1/4

Step-by-step explanation:

Answer:

y=-7/8

Step-by-step explanation:

-4y-10=4y-3

add 10 on both sides

-4y=4y+7

subtract the four on the right from both sides

-8y=7

divide -8 on both sides

answer: -7/8

a rental car company charges drivers a flat fee to rent a car plus $0.25 for each mile they drive. If a drivers pays $100 drives 160 miles , which equation can he use to find his total cost y in terms of the number of miles driven ?

Answers

ANSWER

y = 100 + 0.25(160) - equation

y = 140 - if you needed the answer

what are all values of x for which the series shown converges? ​

Answers

Answer:

One convergence criteria that is useful here is that, if aₙ is the n-th term of this sequence, then we must have:

Iaₙ₊₁I < IaₙI

This means that the absolute value of the terms must decrease as n increases.

Then we must have:

[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}}[/tex]

We can write this as:

[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}} = \frac{(x -2)^n}{(n + 1)*3^n} * \frac{(x - 2)}{3}[/tex]

If we assume that n is a really big number, then:

n + 1 ≈ 1

And we can write:

[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2)^n}{(n)*3^n} * \frac{(x - 2)}{3}[/tex]

Then we have the inequality

[tex]1 > (x - 2)/3[/tex]

And remember that this must be in absolute value, then we will have that:

-1 < (x - 2)/3 < 1

-3 < x - 2 < 3

-3 + 2 < x < 3 + 2

-1 < x < 5

The first option looks like this, but it uses the symbols ≤≥, so it is not the same as this, then the correct option will be the second.

Find the value of X


Answers

Answer:

7

Step-by-step explanation:

Since the smaller triangle is similar to the larger, then its' sides are in the same proportion. So:

1/2=2x-6/16

Then:

4x-12=16

4x=28

x=7 ........................

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