Answer:
f(x)=a(x - h)2 + k
Much like a linear function, k works like b in the slope-intercept formula. Like where add or subtract b would determine where the line crosses, in the linear, k determines the vertex of the parabola. If you're going to go up 2, then you need to add 2.
The h determines the movement horizontally. what you put in h determines if it moves left or right. To adjust this, you need to find the number to make the parentheses equal 0 when x equals -2 (because moving the vertex point to the left means subtraction/negatives):
x - h = 0
-2 - h = 0
-h = 2
h = -2
So the function ends up looking like:
f(x)=a(x - (-2))2 + 2
Subtracting a negative cancels the signs out to make a positive:
f(x)=a(x + 2)2 + 2
Step-by-step explanation:
The translated value of the function is h ( x ) = ( x + 4 )² - 7
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x²
we can obtain the function h(x) by first translating it 4 units to the left, which gives us f(x + 4), and then translating it 7 units down, which gives us f(x + 4) - 7. Therefore, the function h(x) can be written as:
h(x) = f(x + 4) - 7
To write this in vertex form, we need to complete the square. First, we have:
h(x) = f(x + 4) - 7
h(x) = (x + 4)² - 7
This is the vertex form of the equation for h(x). The vertex of the parabola is at the point (-4, -7), which is obtained by setting x + 4 = 0 in the equation above.
The value of the vertex is -7, which is obtained by subtracting 7 from the squared term.
Therefore, the vertex form of the equation for h(x) is:
h ( x ) = ( x + 4 )² - 7
Hence , the transformed function is h ( x ) = ( x + 4 )² - 7
To learn more about transformation of functions click :
https://brainly.com/question/26896273
#SPJ2
HELP ASAP ASAP!! NO LINKS PLEASEEEE OR U WILL BE REPORTED, I NEED AN ANSWER, WILL GIVE BRAINIEST!!
Step-by-step explanation:
1. Image of A is, A' (-7,-2)
2. Pre image of B' is, B (6,6)
3. Image of C is, C' (-3,-5)
4. The side which is congruent to side AB is, A'B'
5. The angle that is congruent to angle C is C'
6. The translation is 9 units left and 6 units down, so (x,y) becomes (x',y') where x' = (x-9) and y' = (y-6)
7.
a. The translation is 2 units right and 8 units down,
so, P (x,y) to P' (x+2,y-8)
b. Quadrilateral PQRS becomes P'Q'R'S' where the translation is 2 units right and 8 units down. Both quadrilateral are same in shape, length and size, their co-ordinates are different, their co-ordinates translated as follows,
P (-4,5) to P' (-2,-3)
Q (0,5) to Q' (2,-3)
R (2,1) to R' (4,-7)
S (-4,1) to S' (-6,-7)
Answered by GAUTHMATH
Nick went canoeing on the river. He traveled 1 mile in 17 minutes. At this rate, how far will he travel in an hour and 25 minutes?
Answer:
5 miles
Step-by-step explanation:
I hope this helps :)
Mariana adoçou um suco com 1/4 de xícara de açúcar. Ao experimentar percebeu que não estava doce como gostaria e acrescentou mais 1/4 de xícara de açúcar. Quanto de açúcar Mariana colocou no suco? *
a) 1/8 xíc. de açúcar.
b) 1/4 xíc. de açúcar.
c) 1/2 xíc. de açúcar.
d) 2/8 xíc. de açúcar.
Answer: B 1/4 doc. de açúcar.
SHOW YOUR WORK
Can someone help?
(no files or links)
(Will give brainliest)
Truck A leaves station 1 at 9:00 a.m. and travels at the rate of 60 kph. After 2 hours, Truck B leaves the same station and travels in the same direction at the rate of 80 kph. At what time will Truck B overtake Truck A?
Answer:
12.30 P.M.
Step-by-step explanation:
Find the area of the shaded region.
help pls
Answer:
1. 50 m
2. 80 cm
Step-by-step explanation:
1. There are 2 triangles, subtract the area of 1 of them from the other.
The triangle that needs to be subtracted: b = 20 m, h = 10 m
A = 1/2b * h = 1/2(20) * 10 = 10*10 = 100 m
The big triangle, the one that needs to be subtracted plus the one you need to find the area of: b = 20 cm, h = 15 cm, 1/2(20) * 15 = 10 * 15 = 150
150 - 100 = 50 c
2. Divide it into 3 parts:
1- 3*4 = 12
2. 7*(4 + 4) = 7*8 = 56
3. [(4 + 4) * (13 - 7 - 3)]/2 = (8*3)/2 = 24/2 = 12
12 + 56 + 12 = 80 cm
PLS HELP!! /BRAINLIST (DONT PUT AN RANDOM ANSWER) PLS HELP ASAP
also if u just put anything I'll report you
Answer:
Step-by-step explanation:
2(2 color pants)*4(4 colored shirt)*2(2 colored tie)=16
Tree diagram below:
screenshot down below
Answer:
82
Step-by-step explanation:
Vertical rectangle:
A = bh
A = (5)(10)
A = 50
Horizontal rectangle:
h = 10 - (3 + 3)
h = 4
A = bh
A = (8)(4)
A = 32
Combined:
50 + 32
82
Answer:
[tex]A=82 meters^2[/tex]
Step-by-step explanation:
First we will split the shape into two rectangles.
Now that it is in two separate peaces, solve each one individually
Remember [tex]A = l*w[/tex]
[tex]10*5=50[/tex]
[tex]8*4=32[/tex]
Finally add the two areas together
[tex]50+32=82[/tex]
Veronica used a copy machine to make an enlargement of a triangle. The original triangle has side lengths of 6 centimeters comma 8 centimeters comma and 10 centimeters. The copy has side lengths of 7.2 centimeters comma 9.6 centimeters comma and 12 centimeters.
Which scale factor did Veronica use to make the enlargement?
Answer:
1.2
Step-by-step explanation:
dsjihgnvosjdiufabnvoilasdb ill give brainley
Answer:
-876 would be the right answer
4x4 Thhhhhhaaannkkkk uuuuu
Answer:
16
Step-by-step explanation:
4+4+4+4
or
8+8
Answer:
16
Step-by-step explanation:
PLZ HURRY! Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts. What percent of the new mixture if peanuts?
Answer:
34%
n = new % = Answer
(4kg x 16%) + (12kg x 40%) = (New Percentage(Total kg))
(.16 x 4) + (.4 x 12) = n(4 + 12)
Simplify above to get:
.64 + 4.8 = 16n
.64 + 4.8 = 5.44
5.44 = 16n
Divide both sides by 16
.34 = n
34%
Convert .34 to Percentage by moving decimal to the right 2 times.
MaybeKuro
Please help with math again! ToT (10 points, link = report to moderators)
Answer:
10.D
Step-by-step explanation:
A=2(wl+hl+hw)
SA=(6,4*4)*2+(6,4*10,5)*2+(4*10,5)*2=269,6 square centimeters
I believe,this is it.
Since it is a juice box the dimensions fit to fold the box,so it's easy to guess looking the parts that need to match together.(I wrote on the image the dimensions that were ''lacking''...)
Pleasee its pretty easy someone helpp
Answer:
81.5, 9, 180
Step-by-step explanation:
28.
c=9
9x9=81
a=1/2
81+1/2=81.5
29.
9x1/2=4.5
4.5x2=9
30.
15x15=225
9x5=45
225-45=180
hope this helps!!!
Which number sequence follows the rule multiply by 3, starting from 4?
A) 3, 6, 9, 12, 15
B )3, 9, 27, 81, 243
C) 4, 12, 36, 108, 324
D) 4, 7, 11, 14, 18
Answer:
c
Step-by-step explanation:
easy no promble at alll
The number sequence follows the rule multiply by 3, starting from 4 are 4, 12, 36, 108, 324. That is option C.
What is rule multiply by a number ?The rule multiple by any number is the sequence of number that are arranged in such a form that the next number to an integer is times the particular given number of the multiple.
From the question,
4 × 3 = 12
12 × 3 = 36
36 × 3 = 108
108× 3 = 324
Therefore, the number sequence follows the rule multiply by 3, starting from 4 are 4, 12, 36, 108, 324.
Learn more about number sequence here:
https://brainly.com/question/6561461
#SPJ2
help me with this question
WhiCh statement is true
PLEASE SOLVE RXU FOR BRAINLIEST :)
Answer:
its 37 lol
Step-by-step explanation:
A doll house is created by modeling a family home. Everything in the doll house is created to scale. If the height of a desk in the family home is 36 inches and the height of the model desk is 1.5 inches, what would the height of a bed be if the bed in the family home is 24 inches tall?
Last year, the ratio of the number of boys to the number of girls in the computer Club 1 : 2. This year, 70 new members joined the computer Club. There are now four times as many boys and three times as many girls as last year. How many members were in the computer club last year?
WILL GIVE BRAINLIEST. 10 POINTS. PLS SHOW WORK.
Answer:
30
Step-by-step explanation:
I hope this is correct, if not please feel free to correct my mistake. I'm sorry in advance if this is an incorrect answer.
Find the lateral surface area of the cylinder. Round to the nearest hundredth if necessary.
Last one!!!
Answer: 353.25
Step-by-step explanation:
2πr^2+2πrh
2(3.14)(4.5)^2+2(3.14)(4.5)(8)
2(3.14)(20.25)+2(3.14)(36)
2(63.585)+2(113.04)
127.17+226.08
353.25
Answer:
353.43 meters squared
Step-by-step explanation:
Surface area = 2πr^2 +πdh
2·π·4.5^2 + π·(9) (8)
127.2345 + 226.1946
= 353.4291
Round to the nearest hundredth: 353.43 meters squared
Consider this rectangle.
The perimeter is P = 2(3) + 2(6) = 18 cm.
Suppose the dimensions of the rectangle are all multiplied by 4.
The new rectangle would have the dimensions _____
The perimeter of the new rectangle would be _ cm.
The new perimeter will be ___ times as large as the perimeter of the original rectangle .
Answer:
new dimentions = 12, 12, 24, 24
new perameter = 72cm
new perameter will be 4 times as large as the original
Step-by-step explanation:
2(3*4) + 2(6*4) = 24+48 = 72
72/4 = 18
The new rectangle would have the dimensions 12 cm and 24 cm
The perimeter of the new rectangle would be 72 cm
And, The new perimeter will be 4 times as large as the perimeter of the original rectangle .
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The perimeter of rectangle is,
⇒ P = 2(3) + 2(6) = 18 cm.
Now, After multiplied by 4 in all the dimensions we get;
Dimensions are,
⇒ 4 × 3 = 12
⇒ 4 × 6 = 24
Hence, The perimeter of the new rectangle would be;
⇒ 2 (12 + 24)
⇒ 2 × 36
⇒ 72 cm
⇒ 18 × 4 cm
Thus, The perimeter of the new rectangle would be 72 cm
And, The new perimeter will be 4 times as large as the perimeter of the original rectangle .
Learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ7
Identify each triangle with its most specific name and explain how you know:
Answer:
Left triangle is scalene, middle is equalaterial, right is isosolece.
Step-by-step explanation:
Scalene traingles have three different angles, and no sides are the same. Equalateral on the other hand have all congruent (equal) angles, and isosolece triangles have two equal sides and two equal angles.
Due in 5 min pls help
Answer:
Step-by-step explanation:
12 or 3
Who ever answers first gets a brainliest A rectangular prism is 14 feet long and 10 feet high. Its volume is 1,680 cubic feet. What is the width of the rectangular prism?
Answer:
The width is 12 feet.
Step-by-step explanation:
If you divide 1,680 by 14 it will give you 120 then divide that by 10 it will give you 12 ft.
The measures of two angles of a triangle are 75 and 62º. Find the measure of the third angle.
13°
c. 470
b. 43°
d. 137
Answer: B 43
Step-by-step explanation:
Well for a triangle it has to be equal to 180 so you would add 75 and 62 to get 137 so you would add each answer to 137 and whichever one equals 180 is the answer therefor stating that the answer is B 43.
I need help please this due in 6 minutes
Answer:
First one
Step-by-step explanation:
Take Square root of 64/9 which is 8/3.
8/3 is greater than 7/3
Hence,
Square root 64/9 > 7/3
A rectangle plot of land is 0.4 kilometres long and 0.07 kilometres wide. What is its area in square kilometres? show your reasoning.
Convert the decimals to fractions, then convert your answer back to decimals
Answer:
I think the answer is 0.28 or 7/25
Step-by-step explanation:
Answer:
0.028 square kilometres
Step-by-step explanation:
The area of a rectangle is:
length x width
The given length is 0.4 kilometres and the given width is 0.07 kilometres.
0.4 x 0.07 = 0.028
So the area of the rectangular plot land is 0.028 square kilometres
Hope this helps!
what is the value of x in the figure ?
plz i beg help i will give brainlist and 21 point
Pls help ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!11
Answer:
42
Step-by-step explanation:
Divide it into 2 parts: 1*12 and (12*5)/2
1*12 = 12
(12*5)/2 = 60/2 = 30
30 + 12 = 42