The function f(x) = x2 6x 3 is transformed such that g(x) = f(x − 2). find the vertex of g(x). (−1, −8) (−3, −4) (−1, −6) (−5, −6)
Answers
Answer: (-1,-6)
Step-by-step explanation:
x^2+6x+3
g(x) = f(x-2)
replace all value of x in the f(x) function to (x-2)
(x-2)^2 + 6(x-2) + 34
(x-2)(x-2) + 6(x-2) + 34
expand through FOIL and distribution
x^2-4x+4+6x-12+3
combine like terms
x^2+2x-5
-b/2a = x value of vertex
-2/2(1) = x value
x value = -1
plug in -1 for all values of x in the g(x) equation to solve for y value
(-1)^2+2(-1)-5
1-2-5 = -6
y = -6
x = -1
(x,y) = (-1,-6)
The vertex of the considered function g(x) = f(x − 2) is given by: Option c: (-1,-6)
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
This point (h,k) is called the vertex of the parabola that quadratic equation represents.
How to convert the given equation to vertex form?We first take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.
So, we're given that:
[tex]f(x) = x^2 + 6x + 3[/tex][tex]g(x) = f(x-2)[/tex]Thus, we get:
[tex]g(x) = f(x-2) \\g(x) = (x-2)^2 + 6(x-2) + 3 \\g(x) = x^2 -4x + 4 + 6x - 12+3\\ g(x) = x^2 + 2x -5[/tex]
Converting g(x) to vertex form:
[tex]g(x) = x^2 + 2x - 5\\g(x) = x^2 + 2x + 1 - 1 -5\\g(x) = (x+1)^2 -9\\g(x) = (x - (-1) )^2 -6\\g(x) = (x-(-1))^2 + (-6)[/tex]
Comparing this with [tex]a(x-h)^2 + k[/tex], we get (h,k) = (-1,-6) as the coordinate of the vertex of the graph of g(x), as shown below.
Thus, the vertex of the considered function g(x) = f(x − 2) is given by: Option c: (-1,-6)
Learn more about vertex form of a quadratic equation here:
https://brainly.com/question/9912128
Related Questions
Solve the equation and show your work.
A . 17x + 12 = 54 - 4x
B . 5x - 10 + 2x = 6(x + 1) - x
Answers
Answer:
A. x= 2
B. x= 8
Step-by-step explanation:
Solving an equation refers to finding the value of the variable in the equation.
A. 17x +12= 54 -4x
Bring all x terms to one side, constant to the other:
17x +4x= 54 -12
21x= 42
x= 42 ÷21
x= 2
B. 5x -10 +2x= 6(x +1) -x
7x -10= 6x +6 -x
7x -10= 5x +6
Bring all x terms to one side, constant to the other:
7x -5x= 10 +6
2x= 16
Divide both sides by 2:
x= 16 ÷2
x= 8
Hey ! there
Answer:
Value of x in equation A is 2 .Value of x in equation B is 8 .Step-by-step explanation:
In this question we are provided with two equations that are 17x + 12 = 54 - 4x and 5x - 10 + 2x = 6(x + 1) - x . And we are asked to solve the equation that means we have to find the value of x for both the equations .
Solution : -
A)[tex] \longmapsto \qquad \: 17x + 12 = 54 - 4x[/tex]
Step 1 : Subtracting 12 on both sides :
[tex] \longmapsto \qquad \: 17x + \cancel{ 12} - \cancel{12} = \bold{54} - 4x - \bold{ 12}[/tex]
Simplifying it ,
[tex] \longmapsto \qquad \: 17x = 42 - 4x[/tex]
Step 2 : Adding 4x on both sides :
[tex] \longmapsto \qquad \: 17x + 4x = 42 - \cancel{4x} + \cancel{4x}[/tex]
On further calculations, we get :
[tex] \longmapsto \qquad \: 21x = 42[/tex]
Step 3 : Dividing with 21 on both sides :
[tex] \longmapsto \qquad \: \dfrac{ \cancel{21}x}{ \cancel{21} } = \cancel{ \dfrac{42}{21} }[/tex]
We get :
[tex] \longmapsto \qquad \: \red{\underline{\boxed{ \frak{x = 2}}}} \quad \bigstar[/tex]
Henceforth , value of x is 2 .Verifying : -
Now , we are verifying our answer by substituting value of x as 2 in the given equation . So ,
17x + 12 = 54 - 4x 17 ( 2 ) + 12 = 54 - 4 ( 2 )34 + 12 = 54 - 846 = 46L.H.S = R.HSHence , Verified .Therefore , our solution is correct .
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
B)[tex] \longmapsto \qquad \: 5x - 10 + 2x = 6(x + 1) - x[/tex]
Step 1 : Adding like terms on left side :
[tex] \longmapsto \qquad \: 7x - 10 = 6(x + 1) - x[/tex]
Step 2 : Solving parenthesis on right side by using distributive property . ( Multiplying 6 with x and 1 both ) :
[tex] \longmapsto \qquad \: 7x - 10 = \bold{6x} + 6 - \bold{x}[/tex]
Step 3 : Solving like terms on right side :
[tex] \longmapsto \qquad \: 7x - 10 = 5x + 6[/tex]
Step 4 : Adding 10 on both sides :
[tex] \longmapsto \qquad \: 7x - \cancel{10} + \cancel{ 10} = 5x + 6 + 10[/tex]
Simplifying it ,
[tex] \longmapsto \qquad \: 7x = 5x + 16[/tex]
Step 5 : Subtracting 5x on both sides :
[tex] \longmapsto \qquad \: 7x - 5x = \cancel{5x }+ 16 - \cancel{5x}[/tex]
On further calculations , we get :
[tex] \longmapsto \qquad \: 2x = 16[/tex]
Step 6 : Dividing with 2 on both sides :
[tex] \longmapsto \qquad \: \dfrac{ \cancel{2}x}{ \cancel{2}} = \cancel{\dfrac{16}{2} }[/tex]
We get :
[tex] \longmapsto \qquad \: \red{\underline{\boxed{ \frak{x = 8}}} } \quad \bigstar[/tex]
Henceforth , value of x is 8 .Verifying : -
Now , we are verifying our answer by substituting value of x as 8 in the given equation . So ,
5x - 10 + 2x = 6(x + 1) - x5 ( 8 ) - 10 + 2( 8 ) = 6 ( 8 + 1 ) - 840 ( - 10 ) + 16 = 6 ( 9 ) - 856 - 10 = 54 - 846 = 46L.H.S = R.H.SHence , Verified .Therefore , our solution is correct.
#Keep Learningwhat is the sum of 1 To 101 only positive integers pease fast
Answers
Answer:
5050
Step-by-step explanation:
sum of first n natural num. = [n(n+1)]/2
sum of first 100 natural num. = (100x101)/2 = 5050
Answer : The sum of 1 to 101 positive integer is 5050
5052 will be sum of 1 to 101 only positive integer
Yo I need to bring up my math grade bad so
y>1/3x
(please show it graphed already :D)
Answers
Answer:
Graph Passing through origin with Gradient ⅓
Step-by-step Solution:
1. Aquire x and y Intercepts by substituting 0 to corresponding value.
When x=0,
[tex]y = \frac{1}{3} (0) \\ y = 0[/tex]
When y=0,
[tex]0 = \frac{1}{3} x \\ x = 0[/tex]
i.e. passing through Origin
do the same for any other 2 points and connect the dots/coordinates and extend the line
Answer number 3 please no bots please I’m just trying to get help.
Answers
Answer:
no 3. is C
no 4. 144 square inch
dhjejdjdoejehdicjf
Pls someone do this its on test
Answers
Answer:
they get a 7/24th piece of cake.
Step-by-step explanation:
if we divide 3 1/2 by 12 we get 7/24
we use the 3 1/2 because that is how many cakes there are.
we use 12 because there are 12 boys that want to split the cake equally.
Given the objective Function: Revenue = 75x+85y and the critical points: (0,0) (180,120) (300,0)
Answers
Answer
(180,120)
Cannot be determined
Step-by-step explanation:
Fax
The critical point with the maximum revenue is at (180,120)
How to determine the critical point with the maximum revenue?The objective function is given as:
Revenue = 75x+85y
The critical points are (0,0) (180,120) (300,0)
Substitute these points in the objective function.
Revenue = 75(0)+ 85(0) = 0
Revenue = 75(180)+ 85(120) = 23700
Revenue = 75(300)+ 85(0) = 22500
The maximum revenue is 23700.
Hence, the maximum revenue is at point (180,120)
Read more about objective function at:
https://brainly.com/question/16826001
PLS HELPPPPP I'VE ASKED FOR FOUR TIMES BUT STILL NO ONE IS WILLING TO ANSWER ME THIS IS SO HARD
35 POINTS WILL BE REWARDED
SOLID AND USEFUL ANSWERS PLS THANKS SO MUCH
here are the answers: (a)(ii) 0.9504 (b) 1/6 (c) 1/31
i just need the steps and it'll be better if you could also type some brief explanations :D
Answers
Answer:
O.9504 is the coreect answer bro
the diameter of a circle is 12 kilometers. What is the length of a 60 degree arc?
Answers
Answer:
Step-by-step explanation:
4 Indira makes a wooden box without a lid. All the faces of the box meet at
right angles. Indira plans to paint all surfaces of the box, including the
inside and outside. The interior of the box has length 13 in., width 8 in., and
depth 7 in. Indira can cover up to 1,350 in.? with
5 cup of paint. Will she
need more than 5 cup of paint to cover the box? Explain how you know.
Answers
Considering the surface area of the rectangular box, it is found that since it is of 502 in² < 1,350 in², she will not need more than 5 cups of paint.
What is the surface area of a rectangular prism?The surface area of a rectangular prism of length l, width w and depth d is given by:
S = 2(lw + ld + wd).
In this problem, we have that the dimensions, in inches, are given by l = 13, w = 8, d = 7. Hence, the surface area in in² is given by:
S = 2(13 x 8 + 13 x 7 + 8 x 7) = 502 in².
Since the surface area of the box is of 502 in² < 1,350 in², she will not need more than 5 cups of paint.
More can be learned about the surface area of a rectangular prism at https://brainly.com/question/17223528
what is the equation of the line that hasthe solution "-2" and 4
Answers
Answer:
First you need to find the slope: (y2 - y1)/(x2 -x1) = (-4 -(-4))/(0-2) = 0. So the line is horizontal, which means the y coordinate is constant and equal to -4, so the equation of the line is y = -4.
Step-by-step explanation:
since both points have a y value of -4 you could have jumped directly to y = -4
PLEASE HELP ASAP FIRST CORRECT ANSWER GETS BRAINLEIST
Answers
k²= 6²+5²
k²= 36+25
k²= 61
k= V61
k=7.81
please help its geometry. Solve for x
Answers
Answer
the answer is x = 9 root 3
Jessica has 573 stickers in her collection. How many sets of 10 stickers does jessica have in her collection?
Answers
Answer:
57 3/10 or 57.3 sets
Step-by-step explanation:
573 stickers divided by 10 sets
Answer:
57 sets of 10 stickers
Step-by-step explanation:
573/10 = 57.3
so, 57 sets of 10 stickers.
Hope this helped! Have a nice day!
Please give Brainliest when possible!
- King Jaron
If the two acute angles of a right triangle are congruent, then what is the measure of each acute angle?
Answers
Nance is riding her bike to a friends house 4 and 1/2 miles away. She’s riding2 and 3/5 miles. How much farther does she need to ride.
Answers
Answer:
1 4/5 miles :)
Step-by-step explanation:
We first need to get them at a common denominator :)
4 1/2 = 4 5/10
2 3/5 = 2 6/10
Now we subtract :)
4 5/10 = 3 14/10
3 14/10 - 2 6/10 = 1 8/10 = 1 4/5
Have an amazing day!!
Please rate and mark brainliest!!
Nance still needs to ride 1 and 9/10 miles to reach her friend's house.
What is speed?Speed is a measure of how quickly an object moves from one place to another. It is defined as the distance traveled by an object per unit of time, and is often represented by the symbol "v". The formula for speed is:
Speed = Distance/Time
Nance is riding her bike to a friend's house that is 4 and 1/2 miles away. She has already ridden 2 and 3/5 miles. To find out how much farther she needs to ride, we can subtract the distance she has already ridden from the total distance:
Total distance = 4 and 1/2 miles
Distance already ridden = 2 and 3/5 miles
Total distance - Distance already ridden
4 and 1/2 - 2 and 3/5 = 9/2 - 13/5 (we need to get a common denominator)
= (45/10) - (26/10)
= 19/10
Therefore, Nance still needs to ride 1 and 9/10 miles to reach her friend's house.
To know more about speed follow
https://brainly.com/question/29150143
#SPJ7
When it is 8:00 a.m. in damascus, it is 4:00 p.m. in vladivostok. if your plane departs from vladivostok at 10:45 a.m. local time and lands in damascus at 12:30 p.m. local time, how long was the flight? a. 1 hour, 45 minutes b. 5 hours, 45 minutes c. 9 hours, 45 minutes d. 13 hours, 45 minutes
Answers
The length of the considered flight in terms of time is given by: Option C. 9 hours, 45 minutes
What is local time?Local time refers to the time of a particular region. The term local refers that whoever is noticing the time and calling it local time means that the person is telling about the time of the place where they're currently staying.
For this case, we're provided that:
When its 8:00 a.m. Damascus it its 4:00 pm in Vladivostok, so the time in Vladivostok is 8 hours ahead of Damascus (or 16 hours behind).
Assuming its 8 hours ahead, as the plane departs from 10:45 am from Vladivostok, and lands in Damascus at 12:30 pm, so 12:30 pm + 8 hours gives 8:30 pm in Vladivostok.
So, the plane departed at 10:45 am of Vladivostok and lands at 8:30 pm in Vladivostok, so it took 9 hours and 45 minutes for his flight to go from Vladivostok to Damascus. (since difference between 8:30 pm and 10:30 am (from 10:30 am to 8:30 pm) is of 9 hours 45 minutes)
Thus, the length of the considered flight in terms of time is given by: Option C. 9 hours, 45 minutes
Learn more about timezones here:
https://brainly.com/question/4054255
Answer:
When it is 8:00 a.m. in Damascus, it is 4:00 p.m. in Vladivostok. If your plane departs from Vladivostok at 10:45 a.m. local time and lands in Damascus at 12:30 p.m. local time, how long was the flight?
a. 1 hour, 45 minutes
b. 5 hours, 45 minutes
c. 9 hours, 45 minutes<<< CORRECT
d. 13 hours, 45 minutes
Step-by-step explanation:
2022 Edge TOPIC TEST
how far away is {-4,-6} away from {5,-6} on a coordinate grid
Answers
Answer:
(-4, -6) and (5, -6) are 9 units away from each other on a coordinate grid.
Step-by-step explanation:
Use the distance formula:
[tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]We are given the points (-4, -6) and (5, -6). Substitute these points into the formula:
[tex]d = \sqrt{(5-(-4))^2+(-6-(-6))^2}[/tex] [tex]d=\sqrt{(5+4)^2+(-6+6)^2}[/tex] [tex]d=\sqrt{(9)^2+(0)^2}[/tex] [tex]d=\sqrt{9^2}[/tex] [tex]d=9[/tex]The distance between (-4, -6) and (5, -6) on a coordinate plane is 9 units.
A Lorry travels for 4 hours at a speed of 58km/h . Work out the travel distance
Answers
Answer: The answer is 9.00988 mi/h
Step-by-step explanation: to be simplified it would be 9.0 or 9 miles an hour
What number is one hundred thousand less than one hundred
million?
Answers
Answer:
900,000
Explanation:
1 million is 10*100,000, so subtracting 100,000 from it is just like subtracting 1 from 10-- just much much larger numbers.
Answer:
99,900,000
Step-by-step explanation:
Less than ⇒ subtraction⇒ Subtract 100,000 from 100,000,000⇒ 100,000,000 - 100,000⇒ 99,900,000What is the average rate of change?
A. 4
B. 2/5
C. 1
D. 2
Answers
Answer:
C) 1
Step-by-step explanation:
The average rate of change remains constant among the 3 given points as [tex]\frac{5-4}{2-1}=1[/tex] and [tex]\frac{10-5}{7-2}=1[/tex], so your answer is C
Anna and Jack make lemonade. Anna uses 2 cups of lemon juice with 9 cups
of
water. Jack uses 3 cups of lemon juice with 15 cups of water. Whose lemonade
has a stronger lemon taste?
Answers
Answer: Anna
Step-by-step explanation:
First, I will create proportions.
Anna: 2 lemon : 9 water
Jack: 3 lemon : 15 water
Next, I will simplify them.
[tex]\frac{2}{9}[/tex] = Already simplified
[tex]\frac{3}{15}[/tex] = [tex]\frac{1}{5}[/tex]
Now I will give them common denominators and compare. Anna's has a larger lemon to water ratio, so Anna's will have a stronger lemon taste.
[tex]\frac{2}{9}[/tex] * [tex]\frac{5}{5}[/tex] = [tex]\frac{10}{45}[/tex]
[tex]\frac{1}{5}[/tex] * [tex]\frac{9}{9}[/tex] = [tex]\frac{9}{45}[/tex]
Find f(-2) for (x) = 3 . 2^x
O A. -36
O B. -12
O c.1/36
O D. 3/4
Answers
[tex]\sf f(x) = 3 \ * \ 2^x[/tex]
insert x = -2
[tex]\sf f(-2) = 3 \ * \ 2^{-2}[/tex]
[tex]\sf f(-2) = 3 \ * \ \dfrac{1}{4}[/tex]
[tex]\sf f(-2) = \dfrac{3}{4}[/tex]
option D. 3/4 will be the correct answer.
[tex]\\ \rm\Rrightarrow f(x)=3.2^x[/tex]
Put -2[tex]\\ \rm\Rrightarrow f(-2)[/tex]
[tex]\\ \rm\Rrightarrow 3.2^{-2}[/tex]
[tex]\\ \rm\Rrightarrow 3(1/4)[/tex]
[tex]\\ \rm\Rrightarrow 3/4[/tex]
Circle Y has an area of 394.38cm ^ 2 . What is the circumference? Use 3.14 for pi Round to the nearest hundredth.
Answers
Answer:
70.38 cm
Step-by-step explanation:
π = 3.14
Area of a circle = πr^2
394.38 = πr^2
125.598726 = r^2
r = 11.2070837 cm
Circumference = 2πr
C = 70.3804856 cm
somebody help me this is hard for me
Answers
Answer:
[tex]\huge\boxed{\bf\: \frac{1}{3}\rightarrow probability}[/tex]
Step-by-step explanation:
Given,
Total number of marbles = 6Number of blue marbles = 2Number of yellow marbles = 1Number of red marbles = 3We are asked to find the probability of choosing a blue marble if they are randomly chosen. Then,
Probabilty of a blue marble
= Number of blue marbles / Total number of marbles
= 2/6
= 1/3
[tex]\rule{150pt}{2pt}[/tex]
Herbert got a 76 on his last unit test. If he increases his score by 30% on the next test, what will his new score be?
Answers
At a carnival game, you may win an inflatable crayon, you may win a small stuffed animal, or you may win nothing at all. If the probability of winning nothing is 0.72 and the probability of winning a small stuffed animal is 0.19, what is the probability of winning an inflatable crayon? Express your answer as a decimal.
A:0.91
B:0.28
C:0.09
D:0.81
Answers
Answer:
C:0.09
Step-by-step explanation:
probability of winning nothing = 0.72 = [tex]\frac{72}{100}[/tex]
probability of winning a small stuffed animal = 0.19 = [tex]\frac{19}{100}[/tex]
probability of winning nothing + probability of winning a stuffed animal
= [tex]\frac{72}{100}[/tex] + [tex]\frac{19}{100}[/tex] = [tex]\frac{91}{100}[/tex]
probability of winning an inflatable crayon = 1 - [tex]\frac{91}{100}[/tex]
= [tex]\frac{100}{100}[/tex] - [tex]\frac{91}{100}[/tex]
= [tex]\frac{9}{100}[/tex]
= 0.09
Find the number that makes the ratio equivalent to 9:4.
72:
Answers
Because 9 x 8= 72 and 4 x 8 is 32
simplify ( 1 - i ) ( 1 - i ) or ( 1 - i ) ^ (2)
Answers
Answer:
-2i.
Step-by-step explanation:
( 1 - i ) ( 1 - i )
= 1(1 - i) - i(1 - i)
= 1 - i - i + i^2
Now i^2 = -1 so we have:
1 - 2i - 1
= -2i
what is another formula for finding the rate of discount?
Answers
Answer:
Subtract the final price from the original price. Divide this number by the original price. Finally, multiply the result by 100.
Step-by-step explanation:
PLSSSSS HELP!!!!
I WILL GIVE BRAINLIEST!!!!
Answers
Answer:
2.924
Step-by-step explanation:
First you'll solve the parenthesis:
...- (5.5-5.5)
...-(0)
Now solve the equation:
[tex]\sqrt[3]{5^{2} - 0}[/tex]
[tex]\sqrt[3]{25}[/tex]
Now solve fully
I hope this helps :)
Answer:
the answer is 3 times the square root of 27
Step-by-step explanation:
