How does graph y=-3(x+1)2 -1 transforms from the parent function y=x^2?
Answers
Given:
The function is:
[tex]y=-3(x+1)^2-1[/tex]
The parent function is:
[tex]y=x^2[/tex]
To find:
The transformation of the given function from the parent function.
Solution:
The transformation of a function is given by:
[tex]g(x)=kf(x+a)+b[/tex] .... (i)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If k<0, then the graph of f(x) is reflected across the x-axis.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
The given function can be written as is:
[tex]g(x)=-3(x+1)^2-1[/tex]
Let the parent function be [tex]f(x)=x^2[/tex], then
[tex]g(x)=-3f(x+1)-1[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]k=-3,a=1,b=-1[/tex]
Therefore, the graph of parent function is stretched vertically by by factor 3 and reflected across the x-axis because [tex]k=-3[/tex], after that the graph of the function shifts 1 unit left and 1 unit down to get the graph of given function.
Related Questions
48 > -6x
A. X > -8
B. X > 54
C. X < -8
D. X < 54
Answers
Answer:
The answer is C.
Step-by-step explanation:
First divide both sides by -6.
48/-6 > x/-6
Remember, you switch the signs if you are dividing by a negative number.
The final answer will be x<-8.
Hope this helps!
a number is at least 16
Answers
A ball bounces to a height of 6.7 feet on the first bounce. Each subsequent bounce reaches a height that is 81% of the previous bounce. What is the height, in feet, of the sixth bounce
Answers
After solving, the height in feet of the sixth bounce is 1.892 feet.
In the given question, we ave to find the height, in feet, of the sixth bounce.
From the given question,
Height on the first bounce = 6.7
Subsequent bounce reaches a height of the previous bounce = 81%
Suppose the height is h.
So according to the question:
h(6) = height on the first bounce*(subsequent bounce reaches a height of the previous bounce)^6
h(6) = 6.7*(81%)^6
h(6) = 1.892 feet
So the height of sixth bounce is 1.892 feet.
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I need help with this, pls answer quick!
Answers
Answer: the answer is 5
Step-by-step explanation:
17-(6*2)
17-12
A parallelogram has three of its vertices at $(-1,0)$, $(2,4)$ and $(2,-4)$. What is the positive difference between the greatest possible perimeter and the least possible perimeter of the parallelogram
Answers
The difference in perimeters is 6.
We have 3 possible points for the last vertex.
These are
[ -1 + 2 , 0 + 4 ] - [ 2 , -4 ] = [ [ 1 , 4] - [2 , - 4 ] = ( -1, 8 )
The perimeter of this parallelogram = [tex]2 [ \sqrt{(-1-2)^{2} + (8-4)^2]} + 8][/tex]
= [tex]2 [ \sqrt{9+16}+ 8 ][/tex]
= 2 [ 5 + 8 ]
= 26
Another possible point is
[ 2 + 2, 4 - 4] - [-1,0] = [ 4, 0] - [ -1,0] = (5,0)
The perimeter of this parallelogram
= [tex]2 [ \sqrt{(5-2)^{2} +(0-4)^{2} } + \sqrt{(2+1)^{2}+ (4-0)^{2} } ][/tex]
= [tex]2 [ \sqrt{3^{2}+ 4^{2} } + \sqrt{3^{2}+ 4^{2} }][/tex]
= [tex]2(\sqrt{25} +\sqrt{25})[/tex]
= 2(5 + 5)
= 20
The third feasible point won't change either the largest perimeter of 26 or the smallest perimeter of 20; therefore, we don't need to calculate it.
Difference = 26-20
= 6
Hence, the difference in perimeters is 6.
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How many solutions does 5x 2y =- 7?
Answers
There is no single answer to this question. It depends on what values are chosen for x and y , equation has an infinite
The equation 5x + 2y = -7 is an indeterminate equation with two unknowns, x and y. This means that the equation has an infinite number of solutions, depending on the values of x and y. For example, if x = 3 and y = -2, then the equation would be satisfied. If x = 2 and y = -3, then the equation would also be satisfied. Therefore, the number of solutions for this equation is infinite.There is no single answer to this question. It depends on what values are chosen for x and y.
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what is 60 to the power of 3/2? not sure how to calculate it
Answers
Answer: 108000
Step-by-step explanation: Here's how I got my answer:
So, first, we need to know something. Whenever there's a fraction, you need to do this. I'll show you the numbers for this problem:
(60^3) / 2
So, the numerator goes in parentheses, and the denominator is what we are dividing by. So, 60^3 is the same as 60 x 60 x 60. You'd get 216000. Then, divide by 2 to get 108000. I hope this helps!
TIP: do NOT turn 3/2 into an improper fraction; 1 1/2. You would get a completely different answer.
Find the surface area and round to the nearest hundredths place when necessary.
Answers
Answer:
First lets find the area of the bottom circle:
7.2 is your radius so:
7.2^2 = 51.84 the reason why you square your radius is because thats apart of the formula when finding the are of a circle.
lets continue:
51.84 x 3.14(pi) = 162.7776
Now we need to find the area of the round surface but first we need to find the circumference of one circle and multiply it by the height.
2 x 3.14 x 7.2 = 45.216
Now lets multiply it by the height:
45.216 x 17 = 768.672
Now lets add both areas:
768.672 + 162.7776 = 931.4496 dont forget to round to the nearest hundredths place! 931.4496 rounded up = 931.45 square meters is your answer.
what’s the area of the other figure?
Answers
9514 1404 393
Answer:
12 in²
Step-by-step explanation:
The ratio of areas is the square of the ratio of linear dimensions.
A/27 = (8/12)²
A = 27(2/3)² = 12
The area of the smaller figure is 12 in².
How to get the awnser
Answers
The slope and the y-intercept of the linear function in this problem are given as follows:
Slope: -2.y-intercept: 6.The equation of the linear function in this problem is given as follows:
y = -2x + 6.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope, representing the rate of change of the linear function.b is the y-intercept, representing the value assumed by the linear function when x assumes a value of zero.From the table, we have that when x = 0, y = 6, hence the intercept b is given as follows:
b = 6.
When x increases by one, y decays by two, hence the slope m of the linear function is given as follows:
m = -2.
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find the length of side xx in simplest radical form with a rational denominator.
Answers
For given right triangle, the length of hypotenuse x = 4/√3
Here we have been given a 30° - 60°- 90° right triangle.
A side opposie to angle 60 degrees measures 2 units.
And x is the hypotenuse of right tirnagle.
To find the value of x, consider sine of angle 60 degrees.
sin(60°) = (opposite side of angle 60°) / hypotenuse
From tirgonometric table, sin(60°) = √3 / 2
So, above equation becomes,
√3/ 2 = 2/x
x = 2 × (2/√3)
x = 4/√3
We can see that the value of x is in in simplest radical form with a rational denominator.
Therefore, x = 4/√3
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Determine if the statement below is true or false. Assume x is not equal to 0 2(3 + 5x) = 6 + 5x
Answers
Answer:
This False because 2 x 5 does not equal 5
Step-by-step explanation:
Hope this helps :)
find the value of x. round to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
21.7
Use the cosine function, which is the ratio (adjacent side) / (hypotenuse).
Here we have cos 37 degrees = adj / hyp = 17.3 / x, and so
x 1
------ = -------------------
17.3 cos 37 deg
Then the hypotenuse length, x, is 17.3 / 0.799 = 21.7
Determine the missing angle measure.
Answers
Answer:
19°
Step-by-step explanation:
In this problem, we have complementary angles, which add up to 90° as indicated by the right angle symbol. So, getting x° is as simple as 90°-71°=19°.
Can someone answer this fast. I suck at angles and I’ll give brainliest when I can to whoever can answer this with no link. I’m going to post more questions later as well.
Answers
It's the 4th option.
Step-by-step explanation:
Corresponding angles are congruent, so x =43. I hope this helps, have a great day!
For which values of k the pair of equations KX 3y K − 3 and 12x Ky K have no solution?
Answers
K must be equal to 0, for the pair of equations to have no solution.
For the pair of equations KX + 3y - K = 0 and 12x + Ky - K = 0 to have no solution, the value of K must be such that the two equations have no common solution.
This can be done by equating the two equations and solving for K.
KX + 3y - K = 0
12x + Ky - K = 0
Subtracting equation (1) from equation (2)
11x + 3y = 0
Divide both sides by 3
x + y = 0
Therefore, K must be equal to 0, for the pair of equations to have no solution.
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What is the mean of 17 20 17 33 22 23
Answers
Answer:
22
Step-by-step explanation:
Mean basically just means average. To find the mean, add the numbers together and divide them by the number of numbers.
17 + 20 + 17 + 33 + 22 + 23 = 132
After that, divide by 6 since there are 6 numbers
132 ÷ 6 = 22
-------
Have a good day :)
A certain television is advertised as a 21-inch TV (the diagonal length). If the height of the TV is 13 inches, how wide is the TV? Round to the nearest tenth of an inch.
Answers
Answer:
16.5 inches
Step-by-step explanation:
Use the Pythagorean Theorem
a² + b² = c²
a² + 13² = 21²
a² + 169 = 441
Subtract 169 from both sides
a² = 272
Take the square root of both sides
a = 16.4924225025
Rounded
a = 16.5 inches
Which proportion is solved correctly using cross products?
4/6 = 12/18 = 4x12=9x18
or
4/6 = 12/18 = 4x12=9x12
Answers
The proportion that is solved correct using cross products is given as follows:
4/6 = 12/18 = 4x18 = 6x12
How to solve a proportion applying cross product?A proportion represents a fraction of a total amount, hence it is written as follows:
p = x/y.
In which the terms are given as follows:
x is the numerator of the fraction.y is the denominator of the fraction.For cross products, we have two proportions that are equal, hence the numerator of the first fraction multiplies the denominator of the second fraction, while the denominator of the first fraction multiples the numerator of the second fraction.
The proportion in this problem is given as follows:
4/6 = 12/18.
Hence the cross product is applied as follows:
4 x 18 = 6 x 12
72 = 72 (which is a true statement).
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A construction crew has just finished building a road. The crew worked for 14 days. If they built 2 1/4 kilometers of road each day, what is the total length of road they built? Write your answer as a mixed number in simplest form.
Answers
Answer:
[tex]31\frac{1}{2}[/tex] kilometers
Step-by-step explanation:
what's tan (-90°)............
Answers
Container A is 13 inches by 19 inches by 25 inches. Container B is 13 inches by 13 inches by 31 inches. In cubic inches, how much greater is the volume of Container A.
Answers
Answer:
936
Step-by-step explanation:
First calculate the volume of each container. to calculate volume, multiply the length * width * height.
For Container A, the volume is 13 * 19 * 25 = 6175 inches.
For Container B, the volume is 13 * 13 * 31 = 5239 inches.
6175 - 5239 = 936 so the volume Container A is 936 cubic inches greater than the volume of Container B.
Helpppppppppppppppppppppp
Answers
Answer:
the answer is 59 because you have to simplify no that's the answer
Question
To be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
What is the maximum time (in seconds) that she can take on her last lap and still make the team?
Answers
The maximum time (in seconds) that she can take on her last lap and still make the team will be 52 seconds.
How to calculate the mean?From the information, to be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
The maximum time (in seconds) that she can take on her last lap and still make the team will be:
= (60 × 5) - (63 + 62 + 65 + 58)
= 300 - 248
= 52
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What is the log2 function?
Answers
The log2 function is a mathematical function that returns the logarithm of a given number to the base 2.
It is used to calculate the power to which a number must be raised to get a particular result.
For example, the log2 of 16 is 4, since 2^4 = 16. It can also be expressed as log2 16 = 4. Log2 is used in many areas of mathematics, including number theory, probability theory, and calculus.
It is also used in computer science and engineering to solve complex problems. Furthermore, it is used in cryptography to calculate the key sizes of encryption algorithms. In general, it is an essential tool for solving mathematical and scientific problems.
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Can you pls help i am giving out brainiest plus you will have 100 points
Answers
Answer:
Wait,
Step-by-step explanation:
Where are Part A and Part B? It doesn't show the questions, just the graph.ANSWER CORRECTLY !!!!!!!!!!!!!!! WILL MARK BRIANLIEST !!!!!!!!!!!!!!
Answers
Answer:
x = 541.324
Step-by-step explanation:
Jesse is buying a new cell phone online. It costs 8,835.3 yen (Japanese money). The U.S. dollar is worth 88.353 yen. How much will Jesse's cell phone cost in U.S. dollars?
Answers
Answer:
Cost of cell phone in U.S. dollar = 100 U.S. dollar
Step-by-step explanation:
Given:
Cost of cell phone in yen = 8,835.3 yen
1 U.S. dollar = 88.353 yen
Find:
Cost of cell phone in U.S. dollar
Computation:
Cost of cell phone in U.S. dollar = Cost of cell phone in yen[1 / 88.353]
Cost of cell phone in U.S. dollar = 8,835.3[1 / 88.353]
Cost of cell phone in U.S. dollar = 8,835.3 / 88.353
Cost of cell phone in U.S. dollar = 100 U.S. dollar
Help me with steps pleaseee
Answers
Answer:
Step-by-step explanation:
What is 9 x 7 x 7 x 7 in standard form
Answers
it would be 3,087
--------------------------
have a great morning/afternoon/evening!! <3
- berry
Answer:
9*7^3
Step-by-step explanation: