how to graph transformations of quadratic functions
Answers
Answer:
Shift "h" units to the right, "k" units up, and reflect over the x or y axis when needed.
Step-by-step explanation:
1) I want to talk about reflections first.
Reflections across the x-axis --> [tex]y = ax^2[/tex], a is the coefficient. if a is negative, then the equation should be reflected across the x-axis. This is known as a vertical reflection. Reflections across the y-axis --> [tex]y=a(bx)^2[/tex], b is the coefficient. If b is negative, then reflect the equation over the y-axis. There are cases where the reflection across the y-axis does not change anything. But, let's say its [tex]y=(x-3)^2[/tex]... the reflection across the y-axis is different (that equation is: [tex]y=(-x-3)^2[/tex] )2) Rigid transformations
Horizontal transformations (to the left or right): [tex]y=a(bx-h)^2[/tex], factor out b from "bx-h" and whatever h equals is the units to the right. If h is a negative number, then you move to the left. Vertical transformations (up and down): [tex]y = a(bx-h)^2+k[/tex]... k is just the units up... if k is negative then we move it down.Example (check image for visual)
We transform [tex]y = x^2[/tex] to [tex]y = -(-x-3)^2+3[/tex] , you move right 3, then reflect across the x-axis, then reflect across y-axis, then move 3 up.
--------------------------------------------------------------------------------------------------------------
Note: In the image, the red line is the original function, the blue one is the transformed function. See if you can follow along with the verbal instructions I gave above.
Related Questions
I'm really bad at mathematics. It would be nice if anyone could help me out :) thanks
Answers
A hiker travels 1.13 kilometers south, then travels 2.25 kilometers east. What’s the hiker’s displacement for the trip?
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Answer:
Total displacement = 2.52 kilometers [south east][tex]a^2 + b^2 = c^2\\1.13^2 + 2.25^2 = c^2\\c^2 = 6.3394\\c = 2.52[/tex]
Step-by-step explanation:
By the Pythagorean Theorem:
which net represents this rectangular prism?
Answers
Answer:
Top left
Step-by-step explanation:
a)
3
NIX 01/x
b
b)
=
= 8.5
Answers
Answer:
a = 8.5
Step-by-step explanation:
MARKING BRAINLIEST PLEASE HELP
Answers
So -15x = 90 - 210
-15x = -120
Divide both sides by -15 that equals 8 so the your answer is but if it’s the time before the draining began (I will assume at 0) then the answer would be 3 + 8, it will be 11 hours for it to reach 90
1/3(1/6 + 5/12) - 1/36
Answers
Answer:
1/6
Step-by-step explanation:
Apply the distributive property.
1/3 x 1/6 = 2/36
1/3 x 5/12 = 5/36
Add the products.
2/36 + 5/36 = 7/36
Subtract the result by the 1/36.
7/36 - 1/36 = 6/36
Simplify the fraction.
6/36 = 1/6
-hope it helps
Veronica tried to solve an equation step by step.
8 = y - 4.6
8 + 4.6 = y - 4.6 +4.6 Step one
12.6 = y step two
Which step is wrong or are no steps wrong?
Answers
1)
Which of the following is not a linear equation in one variable?
(a) 32+5 = 0 (b) 3(x+y) = 0 (c) 3x+5 = 0 (d) 3y+5 = 0
Answers
Answer:
letter c is the answer
Step-by-step explanation:
hope it helps you
Answer:
The answer is Option C.) 3x+5 = 0
Step-by-step explanation:
Option A, can't be the answer. It doesn't show a linear graph. Therefore it's incorrect.
Option B, can't be the answer. It doesn't show a linear graph either. This one is also incorrect.
Option C, on the other hand, is correct because it's not a linear equation.
Option D, can't be the answer. It shows a graph, but with a squiggly line. Therefore, this one is also incorrect.
Hope this helps!
Have a nice day/night/afternoon.
(Can you mark me brainliest?)
- ❤ 7272033Alt ❤
Simplify.
(–12x) ÷ (–2)
6x
12x
3x
112x
Answers
hope this helps. leave a comment if you have a question.
Hello there!
Question:-[tex]( - 12x) ÷ ( - 2)[/tex]
This is an algebraic expression.We need to find the result of it.
Solution:-[tex]\sf \longmapsto (- 12x) \div ( - 2)[/tex]
This algebraic expression may be rewritten as:-
[tex]\sf \longmapsto \: \dfrac{ - 12x}{2} [/tex]
Cancel the minus (-) sign:-
[tex]\sf \longmapsto \dfrac{ \cancel - 12x}{ \cancel - 2} [/tex]
Then,cancel 12 and 2 by 2, 12 ÷ 2 results 6. (Don't cancel x):-
[tex]\sf \longmapsto \: \dfrac{ \cancel {12}x}{ \cancel{2}} [/tex]
[tex]\sf \longmapsto6x[/tex]
Option A
______________________________________
Henceforth the value of the algebraic expression is:
[tex]\boxed{\boxed{\displaystyle \huge 6x}}[/tex]
Option A is correct!
______________________________________
I hope this helps!
Please let me know if you have any questions.
~MisterBrian
pls help i’ll try to give brainlist
Answers
Answer:
1.In the early 19th century, Napoleon's occupation of Spain led to the outbreak of revolts all across Spanish America. Miguel Hidalgo y Costilla—“the father of Mexican independence”—launched the Mexican rebellion with his “Cry of Dolores,” and his populist army came close to capturing the Mexican capital.
2.May marks two key anniversaries in the conflict between the United States and Mexico that set in motion the Civil War—and led to California, Texas, and eight other states joining the Union.
On May 13, 1846, the United States Congress declared war on Mexico after a request from President James K. Polk. Then, on May 26, 1848, both sides ratified the peace treaty that ended the conflict.
The conflict centered on the independent Republic of Texas, which opted to join the United States after establishing its independence from Mexico a decade earlier.
The new U.S. president, James K. Polk, also wanted Texas as part of the United States, and his predecessor, John Tyler, had a late change of heart and started the admission process before he left office. Polk and others saw the acquisition of Texas, California, Oregon, and other territories as part of the nation’s Manifest Destiny to spread democracy over the continent.
The U.S. also tried to buy Texas and what was called “Mexican California” from Mexico, which was seen as an insult by Mexico, before war broke out.
Mexico considered the annexation of Texas as an act of war. After a series of border skirmishes, President Polk asked Congress for the war declaration because, under Article I, Section 8 of the Constitution, only Congress could declare war.
In the fighting that followed, the mostly-volunteer United States military secured control of Mexico after a series of battles, and the Treaty of Guadalupe Hidalgo was signed on February 2, 1848.
It was the first large-scale success of a United States military force on foreign soil.
Mexico received a little more than $18 million in compensation from the United States as part of the treaty.
The pact set a border between Texas and Mexico and ceded California, Nevada, Utah, New Mexico, most of Arizona and Colorado, and parts of Oklahoma, Kansas, and Wyoming to the United States. Their transfer to the United States’ control also cut the territorial size of Mexico in half.
On the surface, the war’s outcome seemed like a bonanza for the United States. But the acquisition of so much territory with the issue of slavery unresolved lit the fuse that eventually set off the Civil War in 1861. But the underlying issue was how adding new states and territories would alter the balance between free and slave states was critical.
On the battlefield, Robert E. Lee, Ulysses S. Grant, and Stonewall Jackson were among those who served in the war against Mexico who would later gain prominence in the American Civil War.
what is 174 divided by 74
Answers
Answer:
2.35
Step-by-step explanation:
Answer:
2.35
Step-by-step explanation:
I hope this helps you!
The expression below represents the perimeter of a square in centimeters.
4(6+2.5)
What is the square's perimeter?
Answers
Answer:
34
Step-by-step explanation:
4(8.5) = 34
What is 6 percent of 200 plz show your work
Answers
Answer: 12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
200 * 0.06 = 12
Mrs. Jerry wants her twenty-five students to each have forty-eight buttons to make a craft project. Mrs. Jerry finds buttons in bags at a store. There are fifteen buttons in each bag. How many bags of buttons does Mrs. Jerry need to buy so she has exactly enough buttons for her twenty-five students? Show all your mathematical thinking.
Answers
Answer:
25X48=1200 buttons in all
1200 divided by 15 = 80
She needs to buy 80 bags which totals 1200 buttons
Step-by-step explanation:
Divide 1200 and 15
Answer: 80
State the y-coordinate of the yintercept for the function below.
f(x) = 4x^3-12x^2-x+15
Answers
Answer:
15
Step-by-step explanation:
let y = f(x)
substitute x = 0
y = 4(0)^3-12(0)^2-(0)+15 = 15
10. Mrs. Taylor wants to lay new carpet in the entrance and hallway of her home as shown below. The carpet she selected sells for $2.50 a square foot. How much will it cost to lay the carpet in the entrance and hallway?
Answers
6) A square has an area of 50.4 in? What is its side length (rounded to the nearest whole inch)?
Answers
Answer:
7inches.
Step-by-step explanation:
the properties of a square is that it has the same length and width (and height. but height isn't needed here).
since the area is 50.4 inch^2, square root this value,
[tex]\sqrt{50.4}[/tex]=7inches.
Solve the system of linear equations y= 2x -3Y= x + 6
Answers
Answer:
x=9, y=15. (9, 15).
Step-by-step explanation:
y=2x-3
y=x+6
----------
2x-3=x+6
2x-x-3=6
x-3=6
x=6+3
x=9
y=9+6=15
Complete the sentences below based on the graph of the function.
Please help!
Answers
Answer:
20 km20 km/h5 km/hStep-by-step explanation:
We assume the graph is a plot of Sean's distance from home as he drives to work, works 8 hours, then drives home with a 2-hour stop along the way. It also appears that t is measured in hours after midnight.
The graph shows Sean's distance from home between 9 a.m. and 5 p.m. (t=17) is 20 km. Based on our assumptions, ...
Sean's workplace is located 20 km from his home.
__
Speed is the change in distance divided by the change in time. Between 8 a.m. and 9 a.m. Sean's position changes by 20 km. His speed is then ...
(20 km)/(1 h) = 20 km/h
Sean's speed driving to work was 20 km/h.
__
Between 5 p.m. (t=17) and 7 p.m. (t=19), Sean's position changes from 20 km to 10 km from home. That change took 2 hours, so his speed was ...
(10 km)/(2 h) = 5 km/h
Sean's speed between 5 p.m. and 7 p.m. was 5 km/h.
_____
Additional comment
The units of speed (kilometers per hour) tell you it is computed by dividing kilometers by hours. ("Per" in this context means "divided by".)
While the slope of the line on the graph between 5 p.m. and 7 p.m. is negative, the speed is positive. The negative sign means Sean's speed is not away from home, but is toward home. When the direction (toward, away) is included, the result is a vector called "velocity." Speed is just the magnitude of the velocity vector. It ignores direction.
Which property should Remus use to solve the equation below? 7 q = 49 division property of equality addition property of equality subtraction property of equality identity property of equality.
Answers
Answer:
Division Property
Step-by-step explanation:
He needs to divide both sides by 7 to find the value of q
The division property of equality should Remus used to solve the given equation and this can be determined by using the given data.
Given :
Equation is [tex]7q = 49[/tex].
The following steps can be used in order to determine the property that Remus use to solve the given equation:
Step 1 - Write the given equation.
[tex]7q = 49[/tex]
Step 2 - The arithmetic operations can be used in order to evaluate the given equation.
Step 3 - Using the division property of equality the value of 'q' can be determined.
[tex]q = \dfrac{49}{7}[/tex]
[tex]q = 7[/tex]
Therefore, the correct option is A).
For more information, refer to the link given below:
https://brainly.com/question/11897796
13. A new bank customer with $5,000 wants to open a money market account. The bank is
offering a simple interest rate of 1.3%.
a. How much interest will the customer earn in 10 years?
b. What will the account balance be after 10 years?
2 POINTS
Answers
Answer:
a) 900 dollars
b) 5900 dollars
Step-by-step explanation:
The complete question is
A new bank customer with $5,000 wants to open a money market account. The bank is offering a simple interest rate of 1.8%. a. How much interest will the customer earn in 10 years? b. What will the account balance be after 10 years?
how many cases does he hear per hour?
Answers
Answer:
13
Step-by-step explanation:
5 x 2 2/3
= 5 x 8/3 = 40/3 =13 1/3
So it's basically 13 1/3, but its 13.
equation of the line that passes through (7,-1) and (-3,-1)
Answers
Answer:
y = - 1
Step-by-step explanation:
Note the y- coordinates of both points are equal, both - 1
This indicates the line is horizontal and parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through
The line passes through (7, - 1 ) and (- 3, - 1 ) with y- coordinates - 1 , then
y = - 1 ← equation of line
13. An amusement park drafting engineer must create a small
Ferris wheel with 12 cabs total, each equally spaced apart to
balance the wheel. How many degrees apart should each cab be?
Answers
Answer:
30 degrees
Step-by-step explanation:
a ferris wheel is a circle
the degree of a circle is 360
360/12=30
30 degrees each
A survey of 500 college students moving into their dorm revealed that 425 brought a microwave, 380 brought a video game console, and 50 brought neither a microwave nor game console. A survey participant is randomly selected. Let M be the event the participant brought a microwave and let C be the event the participant brought a video game console. Organize these events in a two-way table. What is the probability that the participant did not bring a microwave or did not bring a console, P(MC or CC)?
0.10
0.29
0.39
0.90
Answers
Answer:
0.90
Step-by-step explanation:
I’m doing the unit test
Answer:
0.29
Step-by-step explanation:
The probability that they brought both is .90
The probability of neither is .29, which is what this question is asking
PLEASE HELP I"LL GIVE BRAINLEAST
Rico paid $180 sales tax on his new $2,400 motorcycle. What was the sales tax percentage rate where he bought his motorcycle?
7.0% tax rate
7.5% tax rate
8% tax rate
6.5% tax rate
Answers
Answer:
7.5 % Tax rate
Step-by-step explanation:
I used used the calculator to figure out the rate
$2,400 X 7.5%= 180
Q). The sum of four consecutive natural numbers is 166. What are the numbers?
Answers
Answer:
see that attachment
I hope it's help you
Let the four consecutive natural numbers are X,X+1,X+2,X+3
Their sum = X+X+1+X+2+X+3 = 4X+6
According to the given problem
Their sum = 166
⇛ 4X+6 = 166
⇛4X = 166-6
⇛4X = 160
⇛X = 160/4
∴ X = 40
X+1 = 40+1 = 41
X+2 = 40+2 = 42
X+3 = 40+3 = 43
The four consecutive natural numbers are 40,41,42,43
also read similar questions: The sum of two prime numbers is 85, what is the product of these two prime numbers? A. 85 B. 91 C. 115 D. 166
https://brainly.com/question/779569?referrer
I do not know how to answer these questions, can someone explain what I would do to solve them?
Answers
Answer:
Step-by-step explanation:
please help me with this
Answers
Answer:
MN=9.1 cm
LM= 9.9 cm
Step-by-step explanation:
helppppppppp[pppppp[pppppppppp
Answers
Answer:A
Step-by-step explanation:i mean that sound logiclity correct