Write a quadratic function to model the graph to the right.

Write A Quadratic Function To Model The Graph To The Right.

Answers

Answer 1

Answer:

f(x) = (x - 2)² + 2

Step-by-step explanation:

The vertex form of the quadratic function is:

f(x) = a(x - h)² + k

where:

(h, k) = vertex

The axis of symmetry is the imaginary vertical line where x = h

a = determines whether the graph opens up or down, and how wide or narrow the graph will be.

h = determines the horizontal translation of the parabola.

k = determines the vertical translation of the graph.

Given the vertex occurring at point (2, 2), along with one of the points on the graph, (4, 6):

Substitute these values into the vertex form of the quadratic function:

f(x) = a(x - h)² + k

6 = a(4 - 2)² + 2

6 = a(2)² + 2

6 = 4a + 2

Subtract 2 from both sides:

6 - 2 = 4a + 2 - 2

4 = 4a

Divide both sides by 4:

4/4 = 4a/4

1 = a

Therefore, the quadratic function in vertex form is: f(x) = (x - 2)² + 2


Related Questions

A filter in the shape of a cone has a diameter of 3 inches and a height of 4 inches.How much liquid can the filter hold without it overflowing?
A) π in³
B) 3π in³
C)12π in³
D)36 π in³
please answer this Thank you

Answers

[tex] \huge ༆ \bf{Answer} ༄[/tex]

The liquid that the cone can store is its volume, So let's calculate the volume of cone

It is given by : -

[tex] \sf \: v = \dfrac{1}{3} \pi {r}^{2} h[/tex]

radius = diameter ÷ 2 = 3 ÷ 2 = 1.5 in

height = 4 inches

[tex] \sf \: v = \dfrac{1}{3} \pi \times 1.5 \times 1.5 \times 4[/tex]

[tex] \sf \: v = \pi \times 1.5 \times 2[/tex]

[tex] \sf \: v = 3\pi \: \: in {}^{3} [/tex]

The liquid that the cone can hold without overflowing is 3π in³

[tex]꧁ \: \frak{Eternal \: Being } \: ꧂[/tex]

Find the surface area of the square pyramid below.

Answers

Answer:

Step-by-step explanation:

Answer:

96 cm or B

Step-by-step explanation:

Base-l*w, 6*6, 36

Side 1-(h*w)1/2, (30)1/2, 15

Side 2-Same as 1

Side 3-Same as 1

Side 4-Same as 1

15+15=30, 15+15=30, 30+30=60, 60+36=96

96 cm

Write y=-3x+2 in standard form

Answers

Answer:

3x+y=2

Step-by-step explanation:

The equation is in slope intercept form.

y=mx+b

Standard form is given by:

ax+by=c

y=-3x+2

3x+y=2

please quick answer i’ll mark brainliest

Answers

Answer:

1.363

Step-by-step explanation:

Area of the sector is x/360 * pi * r^2

A = 40/360 * pi * 7*7

= 1/9 * 22/7 * 49

= 1/9 * 22 * 7

= 17.111111

Area of the triangle OMN = 1/2 ab sin C

so here A = 1/2 * 7 * 7 * sin 40

= 49/2 * sin 40

= 15.748296437320213494904763542728

so, Area of shaded segment is

= Area of sector - area of triangle

= 17.1111111 - 15.748296437320213494904763542728

= 1.363

-2 1/4 - -4/5 Please help me hurry!!!!

Answers

Answer:

-1.45

Step-by-step explanation:

-2 14--4/5=-1.45

Algebra A regular pentagon has once I represented by 3X +2 and another side represented by 2X +5. Find the length of the sides of the pentagon

Answers

Answer:

3x + 2 = 2x + 5

3x = 2x +3

x = 3

3x + 2 =  18

2x + 5 = 11

Step-by-step explanation:

Answer:

3X +2 = 2X +5

grouping of like one's

3X - 2X = 5 -2

subtract

X = 3

Question 2
Find the area of the shaded region. Express your answer in terms of it.
3 in
6 in
-
9 in
O
12 in
18 in
ina

Answers

I’m terms of 12 in is the correct answer.

When Julius crossed the Rubicon, he had with him 3 times as many soldiers as he
needed to conquer Rome. If he had 26,000 soldiers with him, how many were needed
to conquer Rome?

Answers

86,000 :)

hope it helped!

Use a calculator . Round to the nearest tenth of a degree given cos 0=0.8458

Answers

0.8458 rounded to the nearest tenth is 0.8 given cos is 0.696706709347

What are the roots of the equation 4x^2+24x+45=0 in simplest a+bi form?

Answers

Answer:

X=(-1.5, 7.5)

Step-by-step explanation:

Simplifying

4x2 + -24x + -45 = 0

Reorder the terms:

-45 + -24x + 4x2 = 0

Solving

-45 + -24x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.

(-3 + -2x)(15 + -2x) = 0

 

Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying

-3 + -2x = 0

Solving

-3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.

-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0

0 + -2x = 0 + 3

-2x = 0 + 3

Combine like terms: 0 + 3 = 3

-2x = 3

Divide each side by '-2'.

x = -1.5

Simplifying

x = -1.5  

Set the factor '(15 + -2x)' equal to zero and attempt to solve:

Simplifying

15 + -2x = 0

Solving

15 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.

15 + -15 + -2x = 0 + -15

Combine like terms: 15 + -15 = 0

0 + -2x = 0 + -15

-2x = 0 + -15

Combine like terms: 0 + -15 = -15

-2x = -15

Divide each side by '-2'.

x = 7.5

Simplifying

x = 7.5

Solution

x = {-1.5, 7.5}

combine like terms and solve x


12x + 3 - 4x - 6 = 5

5x - 4 + 7 + 6x - 4x = 24

Answers

Answer:

12x + 3 - 4x - 6 = 5

x=1

5x - 4 + 7 + 6x - 4x = 24

x=3

evaluate x-2y when x =0.75 and y =0.96

Answers

Step-by-step explanation:

x = 0,75

y = 0,96

= x - 2y

= 0,75 - 2.0,96

= 0,75 - 1,96

= -1,21

HELP SOMEONE HEEEEEEEEEEEEEEEEEEEEEELP! which graph is the right one?
Which graph represents an exponential function?

Answers

Answer:

The answer is...

Step-by-step explanation:

what is -37x85
what is 28x-43
what is -53x-98

Answers

Answer:

1. -3145

Step-by-step explanation:

I couldnt solve the other one because they don't have a equal sign. Something like 28x-43= ?

Answer:

-37x85= -3145
28x-43=-1204
-53x-98=5194

those are ur answers

Step-by-step explanation:

GIVING BRAINLIEST! PLS SHOW WORK!!

Answers

Answer:

30

Step-by-step explanation:

all traiangles have to same vetec

Answer:

Since the angle on the top is a 90 degree as you might have noticed.

And the other angle is 30 degrees.

Then the last angle should be 60 degrees.

(Because every angle in a triangle should add up to 180 degrees)

I don't know about the measure of the sides tho.

Hope that helps !

nine times a number subtracted from another number​

Answers

9x mean 9 multipled with an unkown number and 9x is subtracted from another unknown number 'y' . you can substitute with any letters you want ,but you have to use two different letters.

Helppp me Please!!!!! :)

Answers

Answer:

[tex]x = 30 \\ y = 10[/tex]

Step-by-step explanation:

[tex]8x + 6y = 300 \\ x + y = 40 \\ 6x + 6y = 240 \\ 2x = 60 \\ = > x = 30 \\ y = 10[/tex]

Help a Brother Out On The evalute expressions

Answers

Answer:

4. - 11

5. 3

6. 14

7. - 60

that it is

A Distributive Property and GCF

56+42

Answers

Answer:

98

Step-by-step explanation:

you at 56 in to 42

Answer:

98

pa brainless

Step-by-step explanation:

please brainless

Which of the following sets of ordered pairs is not a function?

{(-1, 2), (1, 3), (1, 5), (-3, 4)}
{(0, 2), (1, 4), (2, 5), (3, 6)}
{(-4, 3), (-1, 1), (-2, 5), (3, 7)}
{(0, 2), (1, 2), (2, 2), (3, 2)}

Answers

Answer:

1

first choice

Step-by-step explanation:

in a function, the x-value never repeats.

(found in brainly)

6) A truck driver drove 120 miles in 45 mintues. What is the speed of the truck in miles
per hour?

Answers

Answer:

22.5 mph

Step-by-step explanation:

45/120 to find how many miles in one minute

0.375 miles / 1 minute x 60

22.5 miles / 60 minutes

super easy question for 50 points and brainliest

Answers

7 = s²

s = x + 2

7 = (x + 2)²

7 = (x + 2)(x + 2)

7 = x² + 2x + 2x + 4

7 = x² + 4x + 4

x² + 4x = 3

X1=-2-/7,x2=2+/7 is the answer

what is 916 divied by 320

Answers

Answer:

2.8625

This is 916 divided by 320

Answer:

Full Answer - 2.8625

Rounded - About 3

Nearest Tenth - 2.9

Nearest Hundredth - 2.86

Step by Step:

Shown Below  

Hope this Helps

Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score
of a man 72.4 inches tall. (to 2 decimal places)

Answers

Answer:  1.21

Work Shown:

z = (x - mu)/sigma

z = (72.4 - 69.0)/(2.8)

z = (3.4)/(2.8)

z = 1.2142857 .... which is approximate

z = 1.21

Z-score of a man who is 72.4 inches tall is 0.45.

Understanding the concept of the z-score helps us gauge how far a value is from the mean in terms of standard deviations.

A z-score, denoted as , measures the deviation of a data point from the mean in terms of standard deviations. It's calculated using the formula:

= ( - ) /

Where:

- is the value we want to find the z-score for (72.4 inches in this case).

- is the mean of the dataset (69.0 inches).

- is the standard deviation of the dataset (2.8 inches).

Plugging in the values:

= (72.4 - 69.0) / 2.8 = 1.25 / 2.8 ≈ 0.446

Rounded to two decimal places, the z-score is approximately 0.45.

This means that a man who is 72.4 inches tall is roughly 0.45 standard deviations above the mean height of adult men.

In other words, his height is a bit taller than the average height by about 0.45 times the standard deviation.

This positive value indicates that the man's height is above the mean. If the z-score were negative, it would mean the height is below the mean. By using z-scores, we can compare data points from different distributions and understand how unusual or typical a particular value is within its dataset.

Z-scores help us quantify the relative position of a data point, providing a standardized way to interpret its significance in the context of the dataset's characteristics.

In summary, the z-score of a man who is 72.4 inches tall is approximately 0.45, indicating that his height is slightly above the average height of adult men.

To know more about Z-Score here

https://brainly.com/question/33665002

#SPJ3

Consider an economy made up of 100 people, 50 of whom hold jobs, 10 of whom are
looking for work, and 15 of whom are retired. The unemployment rate is approximately:

17 percent

10 percent

25 percent

20 percent

12 percent

Answers

Answer:

20 por cento de cada um , que colocar

The unemployment rate is approximately 17 per cent. The correct option is A.

To calculate the unemployment rate, we need to consider the number of unemployed individuals (those looking for work) divided by the total labour force (those employed plus those looking for work).

Given:

Total population = 100

Employed individuals = 50

Individuals looking for work (unemployed) = 10

Total labour force = Employed + Unemployed

Total labor force = 50 + 10 = 60

Unemployment rate = (Unemployed / Total labour force) x 100

Unemployment rate = (10 / 60) x 100 ≈ 16.67 percent

Rounding to the nearest whole number, the unemployment rate is approximately 17 per cent.

Therefore, the correct answer is option A.

To know more about an expression follow

https://brainly.com/question/31462319

#SPJ2

can one of yall help me pls :)

Answers

Answer:

Omg i love geometry hehe your in luck :D

Step-by-step explanation:

15.65 should be your answer if i have calculated correctly.

What type of function is represented by the table of values below?

A. exponential
B. cubic
C. quadratic
D. linear

Answers

The answer is A. Exponential

COS(α+β); SINα=- 1/3, α IN QUADRANT IV, TANβ=7/3, β IN QUADRANT III

PLEASE, I HAVE BEEN TRYING TO FIND THE ANSWER FOR 3 HOURS, AND I HAVE SPENT LIKE 1000 POINTS

Answers

Recall the angle sum identity for cosine,

cos(α + β) = cos(α) cos(β) - sin(α) sin(β)

Then given sin(α) = -1/3, we have

cos(α + β) = cos(α) cos(β) + 1/3 sin(β)

α is in quadrant IV, so 3π/2 < α < 2π, and so sin(α) is negative and cos(α) is positive. Then from the Pythagorean identity, we get

sin²(α) + cos²(α) = 1

⇒   cos(α) = √(1 - sin²(α)) = 2√2/3

β is in quadrant III, so π < β < 3π/2, so both sin(β) and cos(β) are negative. If we multiply both sides of the previous identity by 1/cos²(α) and replace α with β, we get

sin²(β)/cos²(β) + cos²(β)/cos²(β) = 1/cos²(β)

⇒   tan²(β) + 1 = 1/cos²(β)

⇒   1/cos(β) = -√(tan²(β) + 1) = -√58/3

⇒   cos(β) = -3/√58

Also recall that by definition,

tan(β) = sin(β)/cos(β)

⇒   sin(β) = tan(β) cos(β) = 7/3 • (-3/√58) = -7/√58

Putting everything together, we find that

cos(α + β) = 2√2/3 • (-3/√58) + 1/3 • (-7/√58) = -(6√2 + 7)/(3√58)

or more clearly,

[tex]\cos(\alpha + \beta) = -\dfrac{6\sqrt2 + 7}{3\sqrt{58}}[/tex]

algerbraic expression in shape
ANYONE PLZ HELP GIVING BRAINLIEST ASAP
:)))

Answers

Answer:

C

Step-by-step explanation:

The shape is composed of a square and a semi circle

area of square = a × a = a²

The diameter of the semi circle is c , then radius = [tex]\frac{1}{2}[/tex] c = [tex]\frac{c}{2}[/tex]

area of semi circle = [tex]\frac{1}{2}[/tex] πr² = [tex]\frac{1}{2}[/tex] π × ([tex]\frac{c}{2}[/tex] )² = [tex]\frac{1}{2}[/tex] π × [tex]\frac{c^2}{4}[/tex] = [tex]\frac{\pi c^2}{8}[/tex]

area of shape = a² + [tex]\frac{\pi c^2}{8}[/tex] → C

Please help with this question

Answers

Answer:

The question or equation is not clear.....

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