Mathematics College

The quadratic parent function has been reflected down, stretched vertically by a factor of 1/3, shifted vertically by 9 units and shifted horizontally by -12 units.


1a) write the function g(x) in vertex form

1b) then rewrite the vertex form into standard form

Answers

Answer 1

Answer:

1a) f(x) = -1/3(x + 12)² + 9

1b) f(x) = -1/3x² - 8x - 39

General Formulas and Concepts:

Algebra I

Equality Properties

Expand by FOIL (First Outside Inside Last)

Standard Form: ax² + bx + c = 0

Transformations Graph: f(x) = a(bx - c)² + d

a = vertical shrink/stretch b = horizontal shrink/stretch c = horizontal movement left/right d = vertical movement up/down

Step-by-step explanation:

Step 1: Define

Reflected down and vertically stretched by 1/3:   a = -1/3

Shifted vertically by 9 units:   d = 9

Shifted horizontally by -12 units:   c = -12

Step 2: Write Vertex Form

Define:                    f(x) = a(bx - c)² + d Substitute:              f(x) = -1/3(x + 12)² + 9

Step 3: Write Standard Form

Define:                              f(x) = -1/3(x + 12)² + 9Expand:                             f(x) = -1/3(x² + 24x + 144) + 9Distribute -1/3:                  f(x) = -1/3x² - 8x - 48 + 9Combine like terms:         f(x) = -1/3x² - 8x - 39

And we have our final answers!

Related Questions

which is closer to 0, -24 or 38

Answers

Answer:

-24

Step-by-step explanation:

Although -24 is a negative number, it still is 24 numbers away from zero. 38 is positive and is 38 digits away.

What is the value of sin(t) if Cos(t)=4/5 and t is in quadrant 1

Answers

Answer:

0.6 or 3/5

Step-by-step explanation:

If cos(t) = 4/5, then, taking the arccos of both sides, t ≈ 36.86989765. Taking the sin of that gives you 0.6, or 3/5 in fraction form.

3.5 is the answer for sure

Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes.
If Roni and Allie work together to mow the field, what part of the field would Roni mow?
about 0.52 of the field
about 0.64 of the field
about 0.71 of the field
about 0.87 of the field
Drag each tile to the correct cell in the table.

Answers

Answer:

About 0.71 of the field

Answer:

The answer is .71 of the field

Step-by-step explanation:

Hopefully this helps you

pls mark brainlest

Jeremiah uses
1/3
cups of veggies for every
1/5
cup of dip when making a snack mix. Enter the number of cups of veggies Jeremiah uses for 1 cup of dip.

Answers

1 and 2/3 cups of veggies

1 and 2/3 cups of veggies

PLEASE HELP! THE FIRST PERSON WHO HELPS ME WILL HAVE GOOD LUCK!

Answers

Answer: The 3/8 image will go with the answer 3/4 x 1/2. The The 3/16 image will go with the answer 1/4 x 3/4. And finally, the 4/9 image goes with the answer 2/3 x 2/3. You’re welcome. :)

Step-by-step explanation:

<1 and <2 are supplementary angles . If m<1=77,then m<2=?

Answers

Answer:

m∠2 = 103°

Step-by-step explanation:

Since ∠1 and ∠2 are supplementary angles, together they equal 180. So, you would just subtract 180-77 and get 103. To check if you are correct just add ∠1 and ∠2 ( 77+103) and you'll get 180.

Answer:

Step-by-step explanation:

The sum of two supplementary angles sum up to 180°

Hence <1+<2 = 180°

Given

<1 = 77

Substitute and get <2

<1+<2 = 180

77+<2 = 180

<2 =180-77

<2 = 103°

Hence the measure of <2 is 103°

plz help out with this with steps to I have all of questions like this to answer if u can help with this I would be able to answer the rest it's for my little sis in (6 garde)​

Answers

2 is the ? Answer :)

At 9 o’clock in the morning, the temperature was 29 Fahrenheit it dropped 5 Fahrenheit each hour what was the temperature at 4 o’clock in the afternoon?

Answers

Answer:

-6 degrees fahrenheit

Step-by-step explanation:

7×5=35

29-35=-6

Find the 77th term of the arithmetic sequence
-7, -2, 3, ...

Answers

Answer:

373

Step-by-step explanation:

first you find the difference between the first two numbers so we do -7 minus -2=-5 then plug it in -7+5=-2 now plug in 5 for the next two numbers -2+5=3 so now we know the rule is +5 now we do 5*76=380 then we do -7+380=373

Which statement about the planes is true?

Answers

bruh

why

what

?

osea  si pero al a vez cuando pasa osea si parece pero no lo es pero lo es cuando puede ser

estimate the solution to the system of equations

Answers

omg, I just said the answer was B.

giving brainliest pls help

Answers

Answer:

Given

Step-by-step explanation:

**Tip: Every first statement reason in every proving starts with 'Given'**

what is the percent increase im 13 to 14, round to the nearest percent
please hurry ​

Answers

Answer:

20 percent

Step-by-step explanation:

help plz idk okhehehehehe​

Answers

That is the answer for the first one

What is the answer for 3(x+5)=5x+7

Answers

Answer:

4 = x

Step-by-step explanation:

First, distribute the 3 to the x and 5.

3x + 15 = 5x + 7

Now, subtract 3x from both sides and 7 from both sides.

8 = 2x

Now, divide by 2 on both sides.

4 = x

#teamtrees #WAP (Water And Plant)

The answer is 4=X

3 times X and 5 is 3X+15=5x+7

From there you subtract 3x from both sides and end up with 15= 2x+7

And then you subtract 7 from the 15. Which is 8

Then divide the 8 by 2 which is 4

(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)] =

Answers

Answer:

It may be 220 9/23. If it's wrong sorry lol.

Step-by-step explanation:

I- uhhhhhhhhhh dkkkkk

In ΔPQR, \text{m}\angle P = (4x-14)^{\circ}m∠P=(4x−14)
∘
, \text{m}\angle Q = (5x+6)^{\circ}m∠Q=(5x+6)
∘
, and \text{m}\angle R = (x-2)^{\circ}m∠R=(x−2)
∘
. Find \text{m}\angle R.m∠R.

Answers

Answer:

17

Step-by-step explanation:

The measure of angle R is 17°

What is a triangle?

A triangle is a polygon with three edges and three vertices.

Given is a triangle, PQR and measurements of the angles are given as, m∠P=(4x−14), m∠Q=(5x+6) and m∠R=(x−2)

We know that, the sum of the interior angles of a triangle is 180°

Therefore, ∠ P + ∠ R + ∠ Q = 180°

4x-14 + 5x+6 + x-2 = 180°

10x -10 = 180°

10x = 190°

x = 19°

Now, ∠ R = x-2

∴ ∠ R = 19-2

∠ R = 17°

Hence, the measure of angle R is 17°

For more references on triangles, click;

https://brainly.com/question/2773823

#SPJ2

Which answer shows 8.45x 104 written in standard form?
.0000845
8,450
Ο Ο Ο Ο
84,500
Ο 8,450,000

Answers

Answer: 84,500




Explanation:

Find the 15th term in the arithmetic sequence 7, 10, 13, 16, 19,... Question 4 options: 49 42 35 52

Answers

Answer:

49

Step-by-step explanation:

first you find the difference between the first two numbers so we do 10-7=3, then plug in 3 for the next 2 numbers 10+3=13, so we know our rule is +3 so now we do 3*14=42 then we do 7+42=49

82 added to a number is the same as 36

Answers

Answer:

-46

Step-by-step explanation:

You’re answer will be -46 I’m pretty sure

What is an advantage of renting a place to live?

Answers

From personal experiences, renting instead of owning a house gives me less expenses to worry about. It really depends on your renting agency however, for my family we have never had to worry about the cost of broken appliances (dishwasher, AC, etc), as every-time we have had one break our renting agency has paid for its repair.

Answer:

The main benefits of renting a place of residence is having fewer responsibilities than homeowners since they do not have to deal with maintenance and repairs. It also offers mobility when a location change is necessary or desirable. Taking possession of a rental house is cheaper than buying a home

PLSSS HELPPPPP I WIILLL GIVE BRAINLIEST!!!!!
PLSSS HELPPPPP I WIILLL GIVE BRAINLIEST!!!!!
PLSSS HELPPPPP I WIILLL GIVE BRAINLIEST!!!!!

Answers

Answer: -12/-5x

Step-by-step explanation: use slope formula which is y2-y1/x2-x1

-7-5/-2-3

-12/-5

And then add x after the slope because slopes have x after them

Answer:

Answer:

1. = 1

2. -1/3

Step-by-step explanation:

1. (2,4) and (1,3)

The slope formula is   y2-y1

                                    ---------

                                     x2-x1

__________________________________________________________

y2=3

y1=4

x2=1

x1=2

Therefore, the slope is 1, and the correct answer is 1.

__________________________________________________________

2. (2,7) and (5,6)

The slope formula is   y2-y1

                                    ---------

                                     x2-x1

Therefore, the slope is -1/3, and the correct answer is -1/3.

______________________________________________

Hope this helps!

Step-by-step explanation:

please give brainliest :3

ive never gotten brainliest

78
61
97
74
72
58
87
36
Equal what​

Answers

Answer:

Step-by-step explanation:

78+61+97+74+72+58+87+36= 563

78+61+97+74+72+58+87+36=563

A contractor bought 6.4 ftof sheet metal. She has used 3.7 ft2 so far and has $43.20 worth of
sheet metal remaining. The equation 6.4x - 3.7x = 43.2 represents how much sheet metal is
remaining and the cost of the remaining amount. How much does sheet metal cost per square
foot?
Sheet metal costs $
per square foot.
-need help ASAP- please and thank you

Answers

Answer:

$16

Step-by-step explanation:

To find the cost per square foot we have to solve the given equation for x:

6.4x - 3.7x = 43.2

2.7x = 43.2

Divide both sides of the equation by 2.7 to isolate the x:

2.7x/2.7 = 43.2/2.7

x = 16

The sheet metal costs $16 per square foot.

Hope this helps :)

May u please help me ill give out the brainly

Answers

Answer: The answer that I think is A

sry if wrong

It’s A your welcome

help please, im failing math.

Answers

Answer:

Step-by-step explanation:i think it's the second one

ion know

Rosa purchaded a sofa that was on sale for 20% off. The sofa cost $ 1850. How much does the Sofa cost?​

Answers

1850 + .2x = x
1850 = .8x
2312.50 = x

Answer:

Step-by-step explanation:

370

Please help I will brainliest!! Really urgent!!

Find the difference

and tell you me how you go it, not just the answer please!❤️

Answers

You have to rewrite the expresion without brakets :
5/6x - 7 - 1/2x - 6
Then calculate the difference between the fractions :
1/3x - 7 - 6
Then calculate the difference between 7 and 6
1/3x - 13
Solution : 1/3x - 13

Answer:

1/3x - 1

Step-by-step explanation:

5/6x - 7 -1/2x + 6.          - -6 turns it to +6

5/6x - 7 -3/6x + 6.          Turn 1/2x to 3/6x to make the denominators the same

5/6x - 3/6x -7 + 6

2/6x -1

1/3x - 1

lupita and kevin walk to school.lupita walks 3/5 mi.kevin walks 0.65 mi.who walks a greater distance to school?how much greater?

Answers

Answer:

0.05

Step-by-step explana

a drink recipe calls for lemon juice and apple juice. the equation below represents the proportional relationship between the cups of lemon juice (L) and apple juice (a) in the recipe.

Answers

Answer: ima newbie

Step-by-step explanation:

Always include the steps and/or background required to get to the final answer. Let’s help other people understand and solve future problems on their own. Show all the calculation if it is a numerical question.

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