Use the graph of the function f(x) - (x + 1)2 + 2. Identify the vertex and
the axis of symmetry.
Answers
Answer:
x = –1 AND (-1,2)
Step-by-step explanation:
The axis of symmetry is x = –1
and the vertex is (-1,2)
i know this because the graph is on -1, 2
and I also took the quiz hope it helps ;)
The vertex of the function is (-1, 2).
The axis of symmetry of the function is -1.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = (x + 1)² + 2
f(x) = x² + 2x + 1 + 2
f(x) = x² + 2x + 3
Now it is in the form of ax² + bx + c
a = 1
b = 2
c = 3
The coordinate of the Vertex of the function is (-b/2a, f(x)) = (x, y)
-b/2a = -2/2 = -1
f(x) = (-1)² + 2 x (-1) + 3 = 1 - 2 + 3 = 4 - 2 = 2
Vertex = (-1, 2)
The axis of symmetry is the x-coordinate of the vertex.
= -1.
Thus,
Vertex is (-1, 2).
The axis of symmetry is -1.
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Related Questions
given the rectangular coordinates (-8,15), which of the following polar coordinate pairs represents the same point in radians?
a(17,2.65)
b(-17,-1.08)
c(12.7,2.65)
d(-12.7,-0.49)
Answers
Answer:
1. (x,y)=
2. (3, 480°), (3,-240°), (-3, -60°)
3. (-17, -1.08)
4. on the second circle from the center and 153° clockwise from the horizontal axis
Step-by-step explanation:
took quiz...100%
Identify the end behavior of the function f(x) = 6x^4 - 12x^3 +8x -10
Answers
Answer:
Step-by-step explanation:
This is a quartic equation with a positive coefficient for x^4 so it is shaped like an M xo ir rises to both the left and the right.
vocab word for this definetion
Answers
Answer:
whats the definition?
Step-by-step explanation:
The Bungling Brothers Circus is in town and you are part of the crew that
is setting up its enormous tent. The center pole that holds up the tent
is 70 feet tall. To keep it upright, a support cable needs to be attached to
the top of the pole so that the cable forms a 60° angle with the ground.
a) How long is the cable?
b) How far from the pole should the cable be attached to the ground?
Answers
Answer:
a. 80.83 ft b. 40.42 ft
Step-by-step explanation:
Let h = height of pole = 70 ft, L = length of cable and x = distance of cable on ground to pole and Ф = angle between cable and ground.
a) How long is the cable?
Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and L being the hypotenuse side, by trigonometric ratios,
sinФ = h/L
L = h/sinФ
L = 70 ft/sin60°
L = 70 ft/0.8660
L = 80.83 ft
b) How far from the pole should the cable be attached to the ground?
Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and x being the adjacent side, by trigonometric ratios,
tanФ = h/x
x = h/tanФ
x = 70 ft/tan60°
x = 70 ft/1.7321
x = 40.42 ft
The length of the cable is 80.83 ft and the distance from the pole should the cable be attached to the ground is 40.42 ft and this can be determined by using the trigonometric function.
Given :
The Bungling Brothers Circus is in town and you are part of the crew that is setting up its enormous tent. The center pole that holds up the tent is 70 feet tall. To keep it upright, a support cable needs to be attached to the top of the pole so that the cable forms a 60° angle with the ground.a) The trigonometric function can be used in order to determine the length of the cable.
[tex]\rm sin\theta=\dfrac{h }{L}[/tex]
where h is the height of the pole, L is the length of the pole, and [tex]\theta[/tex] is the angle from the ground.
Substitute the known terms in the above expression.
[tex]\rm L=\dfrac{h }{sin\theta}[/tex]
[tex]\rm L = \dfrac{70}{sin60}[/tex]
L = 80.83 ft.
b) The trigonometric function can be used in order to determine the distance from the pole should the cable be attached to the ground.
[tex]\rm tan \alpha =\dfrac{h}{x}[/tex]
where x is the distance between pole and cable.
Substitute the known terms in the above expression.
[tex]\rm x = \dfrac{70}{tan 60 }[/tex]
x = 40.42 ft.
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It takes me into 30 minutes to walk from home to school when walking at 5 km per hour What is her average cycling speed If it takes her 15 minutes by bike to travel the same distance
Answers
Answer:
10 km/h
Step-by-step explanation:
I'm not really sure about this but no ones answering your question and I wanna help.
So basically to calculate the average speed you need to divide the distance travelled by time taken
But you do not have the distance traveled. But it is mentioned that it takes u 30 minutes to walk from home to school when walking at 5 km/h so to find the distance all you have to do is... 30 x 5 = 150 km
Now that we have the time and distance all we have to do is find the average speed.
Average Speed = distance ÷ time
So 150 ÷ 15 = 10 km/h
Tell whether the angle measures can be those of a triangle.
20°, 160°, 20°
Yes, can be those of a triangle.
No, cannot be those of a triangle.
Answers
No.
The 3 angles of a triangle need to equal 180 degrees.
The sum of the 3 given angles is greater than 180 ( 160 + 20 + 20 = 200) so it cannot form a triangle.
a winter coat was priced at 200. each month for three months, thr price was reduced by 15. how much was the coat reduced in price
Answers
Why: because the starting price is 200. 15*3= 45 dollars taken off in 3 months. $200-$45=$155. Hope this helps!
plz help 5x + 2 = x – 10
Answers
Answer:
x= -3
Step-by-step explanation:
5x + 2 = x - 10
4x + 2 = -10
4× = 10 - 2
4x = -12
x= -3
The checkbook balance of Hercher Company is $1,955.81. The bank statement shows a balance of $3,142.11. The statement shows interest earned of $31.55 and a service charge of $22.80. There is a deposit in transit of $3,991.88. In further analyzing the statement it was discovered that the bank collected a note for $3,100.000. Hercher Co. forgot to deduct a check for $850 during the month. There is a check outstanding for $2,919.43. What is the reconciled balance?
Answers
Answer:
Reconciled balance $3,142.11
Step-by-step explanation:
The computation of the reconciled balance is shown below:
Debit balance as per check book $1,955.81
Add: interest earned $31.55
Collection of note $3,100
Outstanding checks $2,919.43
Less: service charges -$22.80
Less: deposit in transit -$3,991.88
Less: forgot a check -$850
Reconciled balance $3,142.11
The same would be relevant and considered too
Can someone explain why the answer is False. Will Mark brainliest.
Answers
Answer:
Supplementary Angles are 180 degrees. A triangle has 180 degrees. One angle is already 90 degrees, so 2 more angles with 180 degrees is impossible.
Step-by-step explanation:
how do you solve this ?
Answers
Answer:
x = 37 mm
Step-by-step explanation:
using the Pythagorean theorem:
m² = 13² - 5² = 169 - 25 = 144
m = √144 = 12 mm
x² = 12² + 35² = 144 + 1225 = 1369
x = √1369 = 37 mm
Answer:
x=37.3
Step-by-step explanation:
Since we're looking for "x" we need to use "the Pythagorean theorem".
13mm will be our "A" and 35mm will be our "B" will "x" being the hypotenuse.
Since x is the hypotenuse, it needs to be a number greater than 13 and 35.
c=√(a² + b²)
Making it c=√(13² + 35²)
Making C=37.336 or 37.3
Therefore making, x=37.3
HELPPPPPPP PLEASEEEEEEE!!!!!!!!
:((((((
Answers
What is the value of x in the figure below?
Answers
Answer:
B;24
Step-by-step explanation:
Please ASAP let me know the answer!
Answers
ill mark brainliest, question is attached
Answers
Answer:
w=8
Step-by-step explanation:
[tex]72=7w+2w\\72=9w\\\frac{72}{9} =w\\w=8[/tex]
proof:
[tex]72=7(w)+2(w)\\72=7(8)+2(8)\\72=56+16\\72=72[/tex]
Answer:
Simplest-9w=72, w=8
Step-by-step explanation:
7w+2w=9w
72/9=8
w=8
CAN SOMEONE HELP ME FIND THE AREA OF THE LIGHT GRAY PART WITH AN EXPLANATION :)
(IF YOU WANT ME TO GO TO A LINK I'M NOT, SO YOUR ANSWER WILL BE REPORTED IF YOU DECIDE TO INCLUDE ONE)
Answers
Answer:
91 or 525
Step-by-step explanation:
Multiply the objects width (How long it is), times height. For the smaller object inside the bigger object, it is 91. For the bigger object, it is 525.
A rectangular garden has a width of 7x -2 and a length of 3x +10. Find the perimeter.
Answers
=20x+16
Answer:
20x + 16
Step-by-step explanation:
Width (w) = 7x - 2
Length (l) = 3x + 10
Perimeter = 2*(l + w)
= 2* (3x + 10 + 7x - 2)
= 2* (3x + 7x + 10 - 2 ) {Combine like terms}
= 2* ( 10x + 8) {Use distributive property: a(b +c) =(a*b) + (a*c)}
= 2*10x + 2*8
= 20x + 16
The roots of 3x2 + x = 14 are
1. imaginary
2. real,rational,equal
3.real,rational,unequal
4.real,irrational,unequal
Answers
Answer:
3
Step-by-step explanation:
3x2 +x −14 = 0 12 −4(3)(−14) = 1+168 =169 = 132
The roots of 3x² + x = 14 are real, irrational and unequal
What is Quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x, ax² + bx +c=0 with a ≠ 0 .
Given equation is :
3x² + x = 14
3x² + x - 14=0
we have, a=3, b=1 c=-14
D= b²-4ac
= 1²-4*3*(-14)
= 1+168
= 169
As, D>0
Hence, the roots are real.
Now,
x= -b±√b²-4ac/2a
= -1±√169/2*3
=-1±13/6
x= -1-13/6 and x= -1+13/6
x= -7/3 and x= 12/6=2
Hence, the roots are real, irrational and unequal.
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PLEASE HELP I WILL GIVE BRANLIEST
Sarah is self-publishing her 300-page novel and wants to estimate the printing costs.
Answer the questions to estimate the cost of printing a 300-page paperback book.
1. What is the y-intercept for the trend line? What is the real-world meaning of this point?
2. One point on the trend line is (200, 6). Using this point and the y-intercept, find the slope of the trend line. Show your work.
3. What is the real-world meaning.of the slope?
4. Use the slope and y-intercept to write an equation for the trend line in slope-intercept form.
5. Use your equation to estimate the cost of printing Sarah's 300-page book.
Answers
1. Y-intercept b=5
That means it has a 5.00 starting fee.
2. Using the formula (Y2-Y1)/(X2-X1) we will find the slope between the two points.
Point one (X1 and Y1) will be the Y-intercept.
X1,Y1 = (0, 5.00)
Point 2 (X2 and Y2) will be the point on the trend line.
X2, Y2 = (200, 6.00)
Plug in:
(6.00 - 5.00)/(200 - 0) = 00.5 or 1/200.
3. When printing 200 pages each page will cost $.005.
4. .005x+5
5. .005x+5
.005(300)+5=6.5
good luck♡♡!!
Fill in the blank. -6_-1*
>
<
=
Answers
Answer:
<
Step-by-step explanation:
-6 is lower than -1. you can make a little line and count backwards from 0. -1 is closer to 0 than -6 is, therefore -1 being bigger and the sign being <
PLEASE HELP!!!!! (screenshot)
Answers
Answer:
The answer is A. y <= -3x + 3
Three friends ate 3/4 of a pizza. The 3 friends ate
equal amounts. How much of the pizza did each
friend eat?
Answers
Answer:
each friend ate 1/4 of pizza
Step-by-step explanation:
3/4 ÷ 3
= 1/4
help ASAP Ill give you brainliest
Answers
Answer:
none of these
Step-by-step explanation:
There are 3 boys walking
There are a total of 20 people
3/20 = 0.15
That is 15 percent, therefore none of these answers.
Step-by-step explanation:
any has at least one mode
He got a job selling cell phone services. He will be compensated $20 each hour he
works. He also gets a job at a competing cell phone store. His deal is that he will earn
$10 each hour, BUT he will start off with a bonus of $50 at the start of each day.
1) create equations for each man's compensation
2) After how many hours will they earn the same amount?
3) in an 8 hour day, who will earn more? How much more
Answers
Answer:
I think you should go with 3
The price of an mp3 player is reduced by 60%. The expression c – 0.6c represents the sale price. Which represents an equivalent expression to determine the sale price?
Answers
Answer:
0.4c
Step-by-step explanation:
Given that :
Price of mp3 is reduced by 60%
Let initial price of mp3 = c
Discount on price = 60% = 0.6
Discounted price = initial price - discount on price
Discounted price = c - 0.6c
Discounted price = 0.4c
200% of what number is 350?
Answers
Answer:
The answer is 175
Help ASAP Pls! 20 points!
Use a minimum of two sentences to describe the process for writing the ln(x)=5 in exponential form.
Answers
Answer:
In explanation
Step-by-step explanation:
ln(x) = 5
log (base e) x = 5
exponential form is e ^ 5 = x
you should be able to generate 2 sentences from here, hope it helps!
f (x) = -3x + 1
g(x) = x2 + 2x – 5
Find g (f (x))
Answers
Answer: f
= x = − 3 x + 1 = x = 1 4 g = x 2 + 2 x − 5f( x ) = f ( x )
Step-by-step explanation:
A total of 397 tickets were sold for the school play. They were either adult tickets or student tickets. There were 53 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answers
397 total
53 fewer student tickets than adult tickets
Variables: A for adult tickets, S for student tickets
Known Equations:
a + s = 397
a = s + 53
Solving:
2s + 53 = 397 so 2s = 344 so s = 172
s + a = 397
172 + (172 + 53) = 397 so 172 + 225 = 397
Adult tickets sold: 225
Student tickets sold: 172
Consider the graph of the function f(x)=logx.
Match each transformation of function f with a feature of the transformed function.
Answers
Transformation of function f with a feature of the transformed function.
g(x)=-f(x-3) is vertical asymptote of x=3j(x)= f(x+3) is x-intercept of (-2,0)h(x)=3f(x)-3 is domain of (0, ∞)What is asymptote?An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity. There are three types of asymptotes: vertical, horizontal and oblique
Given function is : f(x)= log x
g(x)= -f(x+3)= - log(x+3)g(x)=-f(x-3) is vertical asymptote of x=3
j(x)= f(x+3) = log (x+3) thenj(x)= f(x+3) is x-intercept of (-2,0)
Domain: As (0,∞),{x | x>0}h(x)=3f(x)-3 is domain of (0, ∞)
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Answer:
Step-by-step explanation: