) () = 2 − 6 + 13 Translate f(x) 7 units to the left and down 5 units. Write your new function in vertex form

Answers

Answer 1

Answer:

[tex]y= (x -4)^2 - 1[/tex]

[tex]Vertex = (4,-1)[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x^2 + 6x+13[/tex]

Required

7 units left and 5 units down

First, we have: [7 units left]

The rule is:

[tex](x,y) \to (x-7,y)[/tex]

So, we have:

[tex]f(x) = (x - 7)^2 + 6(x -7)+13[/tex]

Next, we have: [5 units down]

The rule is:

[tex](x,y) \to (x,y-5)[/tex]

So, we have:

[tex]f'(x) = (x - 7)^2 + 6(x -7)+13 - 5[/tex]

[tex]f'(x) = (x - 7)^2 + 6(x -7)+8[/tex]

Rewrite as:

[tex]y = (x - 7)^2 + 6(x -7)+8[/tex]

Expand

[tex]y = x^2 - 14x + 49 + 6x -42+8[/tex]

Collect like terms

[tex]y = x^2 - 14x + 6x -42+8+ 49[/tex]

[tex]y = x^2 -8x +15[/tex]

To write in vertex form, we have

Subtract 15 from both sides

[tex]y -15= x^2 -8x[/tex]

Divide (-8) by 2; Add the square to both sides

[tex]y -15+ (-8/2)^2= x^2 -8x + (-8/2)^2[/tex]

[tex]y -15+ 16= x^2 -8x + 16[/tex]

[tex]y +1= x^2 -8x + 16[/tex]

Expand

[tex]y +1= x^2 -4x - 4x + 16[/tex]

Factorize

[tex]y +1= x(x -4) -4(x - 4)[/tex]

Factor out x - 4

[tex]y +1= (x -4)(x - 4)[/tex]

Rewrite as:

[tex]y +1= (x -4)^2[/tex]

Make y the subject

[tex]y= (x -4)^2 - 1[/tex]

The vertex is:

[tex]Vertex = (4,-1)[/tex]


Related Questions

Help ASAP thank you!

Answers

This is D.5 units
…………….

If 36 ÷ 9 = 4, which numbers could be placed in the blanks in the order shown to create a corresponding multiplication fact? _____ × _____ = _____
A) 4, 9, 36
B) 4, 36, 9
C) 9, 36, 4
D) 36, 9, 4

Answers

Answer:

a. 4×9=36

glad to help!!

Step-by-step explanation:

The model represents an inequality. What is the solution set for the inequality?

Answers

Given:

The figure of an algebraic tiles model of an inequality.

To find:

The inequality for the given model.

Solution:

On the left hand side of the inequality sign in the model we have 8 tiles of x and 12 tiles of 1. So,

[tex]LHS=8(x)+12(1)[/tex]

[tex]LHS=8x+12[/tex]

On the right hand side of the inequality sign in the model we have 12 tiles of -1. So,

[tex]RHS=12(-1)[/tex]

[tex]RHS=-12[/tex]

Now, the inequality for the given model is:

[tex]8x+12\geq -12[/tex]

Therefore, the required inequality for the given model is [tex]8x+12\geq -12[/tex].

If 8 cents are needed to buy 10 pebbles, how many dollars are needed to buy 205 pebbles?

Answers

Answer:

Hello There!!

Step-by-step explanation:

If 8 cents=10 pebbles then do 205 divided by 10 which is 20.5 . So, 8×20.5=164 dollars.

(8×20.5=164) 8 cents=10 (10×20.5=205)

164 dollars=205

Therefore,the answer is 164 dollars.

hope this helps,have a great day!!

~Pinky~

I need help. URGENT

Use the information and the diagram to answer the question:

What is the area of KLM

Answers

Answer:

i think the answer might be D but im not sure

when a number is doubled and then eight added it became 60 what is the number​

Answers

Answer:

26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

Let the number be x.

Now,

2x + 8 = 60

2x = 60 - 8

x = [tex]\dfrac{52}{2}[/tex]

x = 26

Hence, the number is 26.

Please help me I don't understand. If you explain it too it would really help.

Answers

Answer:

12 square feet

Step-by-step explanation:

To find the area of a triangle you have to multiply the base and height and divide it by two

6 * 4 = 24

24 / 2 = 12

Answer:

12sq.ft

Step-by-step explanation:

Area of∆=1/2x base x height

=1/2 x4 x6

=1/2 x 24

=12

MARK ME BRAINLIEST THANKS MY ANSWER PLEASE DO

Please help me I will give branliest! Find the two missing sides and write your answer as in simplified radical form. image attached

Answers

Answer:

x = y = 15[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the sine ratio and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{30}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2x = 30[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

x = 15[tex]\sqrt{2}[/tex]

The triangle is isosceles (45- 45- 90) , then 2 legs are congruent, so

y = x = 15[tex]\sqrt{2}[/tex]

How can you tell from the equation of a rational function if the function has a hole in the graph ( a removable discontinuity) at x, rather than a vertical asymptote? Give an example​

Answers

Consider that,

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

x^2+7x+10 = (x+2)(x+5)

Dividing those expressions leads to

(x^2+4x+4)/(x^2+7x+10) = (x+2)/(x+5)

The intermediate step that happened is that we have (x+2)(x+2) all over (x+2)(x+5), then we have a pair of (x+2) terms cancel as the diagram indicates (see below). This is where the removable discontinuity happens. Specifically when x = -2. Plugging x = -2 into (x+2)/(x+5) produces an output, but it doesn't do the same for the original ratio of quadratics. So we must remove x = -2 from the domain.

A tailor needs to make uniforms for 32 students from a piece of cloth. If the length of that piece 45 3/4m and each student requires 1 1/8m, calculate the length of cloth that would be left

Answers

Answer:

uniform for 1 student = 1 1/8 = 9/8

uniform 32 students = 32 x 9/8 = 36m

Total cloth = 45 3/4 = 183/4 = 45.75m

Cloth left = 45.75 - 36 = 9.75m i hope that helps

the ratio of men to women working for a company is 4 to 7 if there are 231 employees total how many women work for the company.

Answers

Answer:

297

Step-by-step explanation:

A piano instructor charges students a one-time fee for sheet music and an hourly rate for lessons. The graph below shows the total cost for a student who has taken x lessons.

Answers

Relation between fee charged by piano instructor and the lessons has been shown in the graph.
Two points passing through the line are (2, 80) and (4, 140)
Let the one time fee = $b
Hourly charges for the lessons = $x
Equation of the line will be,
y = mx + b
Slope of the line 'm' =
m =
m =
m = 30
y = 30x + b
For point (2, 80),
80 = 30(2) + b
b = 80 - 60
b = 20
Therefore, one time fee charged by the instructor = $20
Since instructor put a coupon to waive off the one time fee, value of the coupon will be = $20

PLZ HELP I BEGG!! 100 POINTS AND BRANLIEST

Answers

Answer:

Vertical angles are opposite angles that are formed from two intersecting lines. From this, the vertical angle to 3 is 5

Answer:

Step-by-step explanation:

<3 is a right angle so its opposite angle is vertical to it. The answer is <5.

I NEED HELP! I HAVE A TEST TOMORROW AND I NEVER PAYED ATTENTION!!! Whats the variable next to the number?? Like 2c or 6y

Answers

Answer:

It means you multiply the number by that variable.

Step-by-step explanation:

This is used to shorten the equation with a variable.  For example, 2c means 2 times c.  6y means 6 times y.  

please help me

no links please and thank you :)

Answers

y = 5/3 - 4 , y-intercept is 4 , slope is 5/3

I've had to repost this question like 4 times because ppl put fake answers, pls put the answer if u know it and dont lie

Answers

Answer:

189.05 ft^3

Step-by-step explanation:

I think this is the right answer but I'm not 100% sure.

So first, you need to find the area of the rectangular prism. 5*5=25, and there are 5 of these rectangles (4 sides and the bottom), so the total is 125 ft^3. I don't think you would include the area of the top, as the top is not flat, and has a pyramid on it.

To find the area of the pyramid, there is a somewhat complicated and long equation that I can't write here, but you can look up the formula for the area of a square pyramid.

The area of the pyramid is around 64.05 ft^3. 125+64.05=189.0500 rounded to the nearest hundredth is 189.05 ft^3.

PLS HURRRY PLSSS HURRYRY

Answers

Answer: 10in^2 or this

Step-by-step explanation: Hope this help :D

Answer:

29

Step-by-step explanation:

2x2=4

5x5=25

25+4=29

Sorry if this didn't help ;(

Please help me asap!​

Answers

Answer:

Let's analyze the example first:

We have:

3, 4, 6      target 42    answer: (3 + 4)*6

If we solve the equation, we get:

(3 + 4)*6 = 7*6 = 42

So, we need to reorder the first 3 numbers in an expression, such that the solution of the expression is the target number.

a) 2, 5, 6     Target 40

We know that 5*8 = 40

and that 2 + 6 = 8

Then the answer is:

(2 + 6)*5

b) 3, 4, 6  target 12

Here we know that 4*3 = 12

and 6 - 3 = 3

Then the answer is:

(6 - 3)*4

c) 4, 6, 10   target 1.

We know that the quotient of two equal numbers is 1.

And 4 + 6 = 10

Then the answer here is:

(4 + 6)/10

d) 3, 5, 6 target 21

We know that 3*5 = 15

And 15 + 6 = 21

Then the answer here is:

3*5 + 6

e) 2, 7, 10  target 6.

Here is a harder one.

We know that 2*3 = 6

And that 10 - 7 = 3

Then the answer ere is:

2*(10 - 7)

f) 3, 6, 15   target  3

Here we can use:

(15 - 6) = 9

And 9/3 = 3

Then the answer is:

(15 - 6)/3

a triangle having no side congruent is called​

Answers

Answer:

A triangle without any congruent sides or angles is called a scalene triangle. When two triangles are congruent it means that they have the same size and shape.

Step-by-step explanation:

A triangle having no side congruent is called​ is called Scalene triangle.

We have a triangle having no side congruent.

We have to identify the name of this triangle.

What is a Triangle ?

A triangle is a plane figure with three straight sides and three angles.

According to question, we have -

A triangle with no side congruent. If all the three sides of a triangle are of same length then it is called congruent triangle. It is also called Equilateral triangle. Similarly, a triangle with none of its sides equal or congruent is called a Scalene triangle.

Hence, a triangle having no side congruent is called​ is called Scalene triangle.

To solve more questions on Scalene triangle , visit the link below -

https://brainly.com/question/10651823

#SPJ6

PLEASE HELP ME I AM BEING TIMED, I WILL MARK THE BRAINLIEST TO WHOEVER GETS THIS RIGHT, WITH AN EXTRA 10 POINTS!

Answers

Answer:

a)9

Step-by-step explanation:

i dont know what b is sorry

Answer: (a) = The gcf of 63 and 36 is 9. (b) = 9 x (7 - 4)

Step-by-step explanation:

Which of the following is closest to the circumference of a circle whose radius is 21 m

Answers

Here Is your answer!!!!

In the LifeSmarts event, students compete

Answers

Answer:

in pairs

Step-by-step explanation:

i just took the quiz

The inverse of y = e^x

Answers

I hope this helps!!!!

Overnight, a pipe cracked and started to leak into a basementThe graph shows the depth of the water in relation to time
A.) How many inches does the water rise each hour?
B.) How deep is the water after four hours?
C.) How long will take for the water to reach a depth of 80 inches?

Answers

Answer:

Each hour the water will rise 10 in. After 4 hours the water will be 40 in deep. It will take 8 hours for the water to reach a depth of 80 in.

which quadrilateral has diagonals that are congruent but do not bisect each other

Answers

C. A rhombus

Hope this helps!

consider the first six terms
in the sequence -11,-4, 3, 10, 17,24

Answers

Answer:

Next term is 31

Step-by-step explanation:

The numbers keep going up by 7.

If this has helped you please mark as brainliest


Help me it says use the figure for 1 and 2











Answers

C is the right answer

Determine the volume of the rectangular prism.

Answers

the volume is equal to 10/7 cm3

Answer:

30/7 x 1/3 = 1 3/7 cm^3

Which of the binomials below is a factor of this trinomial?
4x2 + 21x + 5
A. 4x + 5
B. 4x-1
C. 4x + 1
D. 4x - 5

Answers

Answer:

c

Step-by-step explanation:

Answer:

C. 4x+1

Step-by-step explanation:

John went shopping for a pair of jeans.
The whole store was 40% off. If the
jeans John picked out were originally
$70, how much would the jeans cost with
The discount?

Answers

Answer:

it should be 42 hope it helps

Step-by-step explanation:

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