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.
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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
PLEASE HELP
In 2010, the population of a city was 167,000. From 2010 to 2015, the population grew by 6.3%. From 2015 to 2020, it fell by 4.6%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
Answers
Answer:
1%
Step-by-step explanation:
Round 9.46 to the nearest tenth.
Answers
Answer:
9.50
Step-by-step explanation:
9.46 to the nearest tenth is 9.50,
wherever there is a th after the value name it is the right hand side of the decimal point that you need to round to.
Hope this helps!
Answer 9.5
Step-by-step explanation: i think-
how much coffee is in the cup, it the cup if 7 feet by 7 feet, and 1 cubic foot = 7.48052
How much coffee in the cup, please show how you did it with pi, volume radius etc.
Answers
Answer:
the volume of a cylinder is pi r^2 h = 3.14.(3.5)^2. 5.5=211.55 cubic foot
211.55 x 7.48052 =1583.36 gallons.
Step-by-step explanation:
Johnathan is driving from Houston to Seattle. After 3 hours, he has traveled 150 miles. After 7 hours, he has traveled 350 miles. This information is also represented in the table below.
Driving Time
Time (hr) Distance (miles)
3 150
7 350
10 500
What is Johnathan’s average rate of speed?
Answers
Answer:
50mph
Step-by-step explanation:
first divide 150 by 3 and you get 50
then divide 350 by 7 you get 50
and finally divide 500 by 10 and you get 50
Johnny kicks a ball into the air. Assume the path of the ball can be modeled with a quadratic function. The ball reaches a height of 10 feet and lands on the ground 3 seconds later. Draw and label a graph that models the path of the ball. Write an equation that models the path of Johnny’s ball.
Answers
An equation that models the path of Johnny’s ball is [tex]y = -\frac{40}9(x - 1.5)^2 + 10[/tex]
The maximum height is given as:
[tex]h_{max}= 10ft[/tex]
And the time spent is:
[tex]t = 3s[/tex]
So, the vertex of the ball would be:
[tex]Vertex = (t/2,h_{max})[/tex]
This gives
[tex]Vertex = (3/2,10)[/tex]
[tex]Vertex = (1.5,10)[/tex]
Rewrite properly as:
[tex](h,k) = (1.5,10)[/tex]
The ball is on the floor after 3 seconds.
So, another point on the graph is:
[tex](x,y) = (3,0)[/tex]
A quadratic equation is represented as:
[tex]y=a(x - h)^2 + k[/tex]
Substitute [tex](x,y) = (3,0)[/tex] and [tex](h,k) = (1.5,10)[/tex] in [tex]y=a(x - h)^2 + k[/tex]
[tex]0=a(3 - 1.5)^2 + 10[/tex]
[tex]0=a(1.5)^2 + 10[/tex]
Evaluate the exponent
[tex]0=2.25a + 10[/tex]
Subtract 10 from both sides
[tex]2.25a =- 10[/tex]
Divide both sides by 2.25
[tex]a = -\frac{10}{2.25}[/tex]
Multiply by 4/4
[tex]a = -\frac{40}{9}[/tex]
Substitute [tex]a = -\frac{40}{9}[/tex] and [tex](h,k) = (1.5,10)[/tex] in [tex]y=a(x - h)^2 + k[/tex]
[tex]y = -\frac{40}9(x - 1.5)^2 + 10[/tex]
See attachment for the graph that models the path
Read more about quadratic functions at:
https://brainly.com/question/11441586
how to find vertical asymptotes and horizontal asymptotes
Answers
Answer:
Degree of numerator is less than degree of denominator: horizontal asymptote at y = 0. Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote. Degree of numerator is equal to degree of denominator: horizontal asymptote at ratio of leading coefficients.
Step-by-step explanation: Correct me if i'm wrong lol.
7. Explain what step was taken to go from the first equation to the second equation.
step 1: 2(x - 4) = -12
step 2: 2x - 8 = -12
A. Distribute the 2 on the left side of the equation.
B. Subtract both sides by 4.
C. Divide both sides by 2.
D. Add 4 on the left side.
Answers
Option A
your just multiplying the 2 to what's in parentheses
Troy pays a one-time rental fee of $25 and $15 per day to rent a bicycle.
Write an expression that gives the amount Troy pays to rent
d days
Answers
Answer:
y = 15d + 25 or y = 15x + 25
can someone please help me with this one? I’ve been stuck on it for ages! Tysm if you do!! I appreciate it!
Answers
Answer:
50
110
90
=250
Step-by-step explanation: 90+50+110
I HOPE THIS HELPS
Select all the equations that have {7} as its solution set. 65−2x=6x+9 9−x=14x 3+4x=5x−4 x2+1=8x−5
Answers
Answer:
the answer is this hope it helps im not sure if its all right good luck.
Step-by-step explanation:
A. 65-2x=6x+9
B. 9-x=14x
C. 3+4x=5x-4
d is wrong
The first and third equations have {7} as their solution set.
What is an equation?It is a mathematical statement that is made up of two expressions connected by an equal sign.
The first equation is
65−2x=6x+9
Rearranging the above equation gives
8x = 65-9 = 56
i.e x = 7
Consider the second equation,
9−x=14x
i.e x = 9 / 15 = 0.6
The third equation is:
3+4x = 5x−4
i.e x = 7
The last equation is
x^2+1 = 8x−5
Its solution is not equal to 7.
As a result of the preceding equations, we can conclude that only the first and third equations have "7" as their solution set.
To learn more about equation, use the link given below:
https://brainly.com/question/29538993
#SPJ2
Use the area model to multiply
–
1
4
8q+
1
2
r.
First, find the partial products. Write numbers as integers, decimals, or simplified proper or improper fractions.
Answers
Answer:
no porque algunproblemw
HALPPPPP :(((((((((((
Answers
Answer: 5
Explanation: 12(3) - 3(1/3)/4(3)-5
= 36-1/12-5
= 35/7
= 5
what is 7x5 and ummmmmm
Answers
Answer:
35
Step-by-step explanation:
Answer:
35
Step-by-step explanation:
solve the equation 1 = u over 2
Answers
Answer:
u = 2, as we multiply both sides by the denominator (2).
abebe is 12 years old and his sister aster is 2 years old. In how years abebe be exactly twice as old as aster
Answers
Answer:
8 years
Step-by-step explanation:
Currently
Abebe → 12 years old
Aster → 2 years
With every passing year, each of them will be 1 year older hence the difference between their ages will remain constant.
Difference in ages
= 12 -2
= 10
Let the age of Aster be x years old when Abebe is twice her age.
Abebe → 2x years old
Aster → x years old
Difference in age
= 2x -x
= x
x= 10
Aster is 10 years old when Abebe is twice her age.
Number of years passed
= 10 -2
= 8
Thus, Abebe will be twice as old as her sister in 8 years.
The volume of a cylinder is 600 pi cm cubed. The diameter of a base of the cylinder is 10 cm. What is the height of the cylinder?
Answers
Answer:
V = B * H area of base * height
B = pi * (D / 2)^2 = pi * 5^2 = 78.5 cm^2
H = V / B = 600 cm^3 / 78.5 cm^2 = 7.64 cm
in baseball the home plate is shaped like the one shown it has three right angles and two other congruent angles A and B find measurement of angle a and measurement of angle B
Answers
Answer:
135
Step-by-step explanation:
the triangle is 90-45-45
the square is 90-90-90-90
where the two meet just add 45 + 90
135
there are 47 students in the science club. all but 5 of them went on a field trip to the planetarium. what is the total cost if each student who went on the field trip paid $7?
Answers
Answer:
294
Step-by-step explanation:
40x7=280
2x7=14
280+14=294
Answer:
$294
Step-by-step explanation:
There is a total of 47 students in the science club.
5 did not go on the trip.
Number of students who went on the trip: 47 - 5 = 42
42 students wen on the trip.
Cost per person: $7
Total cost for 42 students: 42 × $7 = $294
John has decided to get in shape for the new year. He is planning to joining the local fitness club. The fitness club charges customers a $14.95 monthly fee plus a one time joining fee $110.00.
What is the total cost John will pay for a 12-month membership at the fitness club?
Answers
To qualify for a scholarship, a student must score at least 90% on a written test. The test is 64 questions. Using this metric, what is the greatest number a student can miss and still qualify for the scholarship?
Answers
Answer:
6 questions
Step-by-step explanation:
First, you divide the total score of 100 by the 64 questions to get 1.5625 points per question. Next, you divide the lowest score to qualify of 90 by the 1.5625 to get 57.6 questions correct to qualify. Then, you round 57.6 questions correct up to 58 questions correct because a fraction of a question correct doesn't make sense. Finally, you subtract the total number of questions (64) by the required correct answers (58) to get 6 questions you can miss to still qualify for the scholarship.
Will mark brainly!! :)
What is the inverse of [tex]f(x)=-2x+7\\[/tex]
[tex]f^{-1} (x) =2x-\frac{7}{2}[/tex]
[tex]f^{-1} (x)=-2x+7[/tex]
[tex]f^{-1} (x)=\frac{1}{2}x-\frac{7}{2}[/tex]
[tex]f^{-1} (x)=-\frac{1}{2} x+\frac{7}{2}[/tex]
Answers
Answer:
[tex] {f}^{ - 1} (x) = - \frac{1}{2} x + \frac{7}{2} [/tex]
Could someone answers these! I Really NEED HELP
Answers
Answer:
(3x + 5) (x - 3)
Step-by-step explanation:
This is the quadratic expression
What type of function is represented in the table? exponential linear quadratic logarithmic
Answers
2022 EDGE ASSIGNMENT
Modeling Functions Using Finite Differences
1. C
2. A, E
3. B
4. B, D
5. D
6. A
7. B, F
1.60x + 0.95(12)=23.40
solve for x
Answers
Eliza fell asleep at 9:35 pm she awoke at 8 hours 45 minutes later what time did she wake up??
Answers
Answer:
6:20 AM
Step-by-step explanation:
Chuy wants to buy a new television. The television costs $1,350. Chuy decides to save the same amount of money each week, for 27 weeks. After 8 weeks Chuy saved $440. Which of the following conclusions can you make about Chuy's plan? a. Chuy has a good plan and will have exactly $1,350 saved at the end of 27 weeks. b. Chuy must increase the amount he saves each week in order to meet his goal at the end of 27 weeks. c. Chuy will save more than he needs and will meet his goal in less than 27 weeks. d. There is not enough information given to make a conclusion about Chuy's plan. Please select the best answer from the choices provided A B C D
Answers
Answer: C: Chuy will save more than he needs and will meet his goal at the end of 27 weeks.
Step-by-step explanation: Divide the amount of money saved, $440, by the number of weeks, 8.
440/8 = $55.
This means $55 is the amount of money Chuy saves every week.
Multiply $55 by the number of weeks Chuy plans to save money, 27.
55 x 27 = 1,485.
Since the television costs $1,350 dollars, Chuy will save more than he needs and will meet his goal in less than 27 weeks.
This is a 45-45-90 triangle.
What is the measure of x?
Х
14
Х
x = [?]V
Answers
Answer:
x = 14[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Since the triangle is 45- 45- 90 then it is isosceles with the 2 legs being congruent, both 14
Using Pythagoras' identity in the right triangle
x² = 14² + 14² = 196 + 196 = 392 ( take square root of both sides )
x = [tex]\sqrt{392}[/tex] = [tex]\sqrt{196(2)}[/tex] = [tex]\sqrt{196}[/tex] × [tex]\sqrt{2}[/tex] = 14[tex]\sqrt{2}[/tex]
NEED HELPPP ASAAPPPPPPP
Answers
Answer:
me too
Step-by-step explanation:
which value of the variable m satisfies the equation 20 = -2(4m - 5)
Answers
Answer:
m = - 1.25
Step-by-step explanation:
20 = - 2(4m - 5) ← divide both sides by - 2
- 10 = 4m - 5 ( add 5 to both sides )
- 5 = 4m ( divide both sides by 4 )
- [tex]\frac{5}{4}[/tex] = m , that is
m = - 1.25
quotient of 2 2/3 and 3 1/2
Answers
Answer:
16/21
Step-by-step explanation: