transforming quadratic graphs

Transforming Quadratic Graphs

Answers

Answer 1

Answer:

f(x) = 3(x - 2)² + 4

OR  

f(x) = 3x² - 12x + 16

Step-by-step explanation:

Vertex form of a parabola:

y = a(x - h)² + k

Standard form of a parabola:

y = ax² + bx + c

Let's find the vertex of this parabola.

(h, k) → (2, 4)

In order to find the a-value (vertex form), let's use another point besides the vertex on the parabola.

Using (3, 7) for (x, y), let's substitute this point and the vertex (2, 4) for (h, k) into the vertex form equation and solve for a.

7 = a[(3) - (2)]² + 4

Simplify using PEMDAS.

7 = a(1)² + 47 = a + 4

Subtract 4 from both sides.

a = 3

Now we have (h, k) and a of the vertex form.

y = a(x - h)² + k  → y = 3(x - 2)² + 4

In order to convert from vertex to standard form, simplify the equation by FOILing.

y = 3(x - 2)² + 4y = 3(x² - 4x + 4) + 4

Distribute 3 inside the parentheses.

y = 3x² - 12x + 12 + 4

Combine like terms.

y = 3x² - 12x + 16

Therefore, we have the answer:

Vertex form:

f(x) = 3(x - 2)² + 4

Standard form:

f(x) = 3x² - 12x + 16

Related Questions

18)
The base of a triangle is 545 cm and the height is 388 cm. What is the area of the triangle? Recall: A-
8y133 cm?
12487 cm?
45\110 cm?
75y22 cm

Answers

Answer:

75y22cm

76c x 34 =876

Step-by-step explanation:

Solve the radical equation. Quick !!! Show work !
-26x + 3 = -18

Answers

Answer:

12

Step-by-step explanation:

[tex]-2\sqrt{6x+3} = -18[/tex]

divide both sides by negative 2

[tex]\sqrt{6x+3} = 9[/tex]

square both sides

6x+3=81

6x=78

x=12

Which of the following best describes the slope of the line below?

Answers

The slope has the run and raise of -2/-2 which it a negative slope

What is the slope and y intercept of Y= -4x + 2

Answers

Answer:

Slope=-4

Y intercept= 0,2

Step-by-step explanation:

Use the slope-intercept form to find the slope and y-intercept.

answers for both boxes please ​

Answers

Answer:

x = -5  y = -3

Step-by-step explanation:

-3x + 2y = 9

multiply the 2nd equation by 3 to set it up for elimination

3(x - 3y)= 3(4)

3x-9y = 12

so now combine both to add

-3x + 2y = 9

3x - 9y = 12

Adding both gives you

-7y = 21

divide both by -7 and you get

y = -3

and you substitute y back into equation to get x

x - 3 (-3) = 4   gives you

x + 9 = 4

x = 4 - 9

x = -5

Can someone please help me. It’s hard and I don’t understand.

Answers

9513 1404 393

Answer:

changes by 120 for each copyis 1800 if none are sold

Step-by-step explanation:

Let's look at the second question first.

x is the number of copies Chau sells. If he doesn't sell any copies, then x = 0. To find Chau's pay, we use x=0 in the equation, and solve for y.

  120×0 +1800 = y

  0 +1800 = y

  1800 = y

Chau's pay when he sells no copies is $1800.

__

If Chau sells 1 copy, then his pay is ...

  120×1 +1800 = y = 1920 . . . . . . . use the equation with x = 1

The increase in Chau's pay is 1920 -1800 = 120.

Chau's pay changes by $120 for each copy he sells.

What property does
(3 + 19) – 12 = 3 + ( 19 – 12)
represent?

Answers

Answer:

associative property

Step-by-step explanation:

The sum of the ages of the father and the mother is
60 years and the sum of the ages of their three
children is 15 years. Find the average age of the
members of the family.​

Answers

Answer:

The average age would be 45.

Step-by-step explanation:

select the correct solution for 6x = 30
(A) x = 24
(B) x = 1/5
(C) x = 5
(D) x = 36

Answers

Answer:

answer is (C) x = 5

I hope it helps you

:-))

There are two ways to solve this u can divide the 30 by 6 (30/6=5) or you can ask yourself what numbers times 6 is equal to 30? 6 time ? =30 which is also equal to 5.
So that would make (c) x=5 the correct answer

i need help on the botto that says What is the cost of buying 10 tickets?

Answers

Answer:

305$

Step-by-step explanation:

305 because if it costs 61 dollars for 2 tickets and 61/2 30.5. 30.5*10=305

4 cm
5 cm
5 cm
5 cm
5 cm
What is the total surface area

Answers

Answer:

24 cm

Step-by-step explanation:

what is the value of x

Answers

Answer:

20

Step-by-step explanation:

because angle 5 is found on the same line as 45 degrees (don't remember what that's called), we can subtract from 180 to find

angle 5 = 135

angle 5 and 5x+35 are alternate interior angles, so they have the same value

135=5x+35

100=5x

20=x

Answer:

Thanks for the points :3


2 + (-10) =
HELP ME PLEASE T^T

Answers

Answer:

The answer would be 8

Step-by-step explanation:

This equals 10-2=8

Answer:

-8

Step-by-step explanation:

If you subtract 10 from 2 you get 8 and since the negative number is greater than the positive number it would be -8

The equation 4s + 3d = 33 is used to determine the number of sandwiches, s, and drinks, d, that can be purchased with $33. If you purchase 3 drinks at $3 each, how many sandwiches will you be able to purchase?

Answers

You will be able to purchase 6 sandwiches at $4 each.

ANSWER FAST ILL GIVE BRAINLIEST!!
Find the surface area of the pyramid to the nearest whole number.

Answers

Given:

A square base pyramid whose base length is 10 in. and height of triangular surface is 4 in.

To find:

The surface area of the pyramid to the nearest whole number.

Solution:

A square base pyramid contains square base with edge 10 in. and 4 congruent triangles with base 10 in. and height 4 in.

Area of a square is

[tex]A_1=(edge)^2[/tex]

[tex]A_1=(10)^2[/tex]

[tex]A_1=100[/tex]

So, area of square base is 100 sq. in.

Area of a triangle is

[tex]A_2=\dfrac{1}{2}\times base\times height[/tex]

[tex]A_2=\dfrac{1}{2}\times 10\times 4[/tex]

[tex]A_2=20[/tex]

So, area of each triangular surface is 20 sq. in.

Now, the total surface area of the pyramid is

Total area = Area of square base + Area of 4 congruent triangles.

[tex]A=A_1+4\times A_2[/tex]

[tex]A=100+4\times 20[/tex]

[tex]A=100+80[/tex]

[tex]A=180[/tex]

Therefore, the area of the pyramid is 180 sq. in.

don’t mind my crusty computer

Answers

Answer:

Okay

Step-by-step explanation:

Answer:

R.I.P adrians hat

Step-by-step explanation:

Round 60958 correct to 1 significant figure

Answers

The answer is 60000 because it is only to 1sf

Answer:

60,000

Step-by-step explanation:

The three angles of a triangle measure x+37, 90, and x+67. Find the measurement of the smallest angle in degrees.

Answers

Answer:

The smallest angle in the triangle is 30°

Step-by-step explanation:

You can solve this by including the fact that the sum of the angles in the triangle has to be 180 degrees. We're given values describing the angles, so we can simply add them together, say the equal 180, and solve for x:

[tex](x + 37) + 90 + (x + 67) = 180\\2x + 37 + 90 + 67 = 180\\2x + 194 = 180\\2x = 180 - 194\\2x = -14\\x = -7[/tex]

The smallest angle then is x + 37, or 37 - 7, giving us 30°

If three angles of a triangle measure x+37, 90, and x+67. Then 30 degrees is the measurement of the smallest angle in degrees.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

The three angles of a triangle measure x+37, 90, and x+67.

We need to find the measurement of smaller angle.

From angle sum property we know that the sum of three angles is equal to 180 degrees.

x+37+90+x+67=180

2x+194=180

Subtract 194 from both sides

2x=180-194

2x=-14

Divide both sides by 2.

x=-7

Substitute the value of x in smallest angle

x+37

-7+37=30

Hence the measurement of the smallest angle in degrees is 30

To learn more on Triangles click:

https://brainly.com/question/2773823

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help me with this math question please

Answers

Answer:

d is correct

Step-by-step explanation:

What is 990-990
I need correct answers only

Answers

Answer:

according to my calculations the answer will be 0

Answer:

990 - 990 = 0

Step-by-step explanation:

 990

 990

- ____

  000

[WILL GIVE BRAINLIIEST! PLEASE HELP!!] In the first week of​ July, a record 1,040 people went to the local swimming pool. In the second​ week, 105 fewer people went to the pool than in the first week. In the third​ week, 145 more people went to the pool than in the second week. In the fourth​ week, 196 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four​ weeks?

Answers

Answer:

13

Step-by-step explanation:

I'm just here for da points can I still get brainliitest?

M is the midpoint if AB . If coordinates of A are (-1,5) and the coordinates of M are (3,3) , what are the coordinates of B?

Answers

Answer:

The co-ordinates of B are ( 7,1)

Step-by-step explanation:

Step(i):-

Given that 'M' is the midpoint of AB

Given co-ordinate points are A(-1,5) and midpoint M(3,3)

we know that the midpoint formula

[tex]midpoint = (\frac{x_{1} +x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )[/tex]

[tex](3,3) = (\frac{-1+x_{2} }{2} ,\frac{5+y_{2} }{2} )[/tex]

Step(ii):-

Equating

        [tex]3 = \frac{-1+x_{2} }{2}[/tex]      and   [tex]\frac{5+y_{2} }{2} = 3[/tex]

cross multiplication, we get

     6 = -1 + x₂    and  6 = 5 +y₂

     x₂ = 6+1        and y₂ = 6-5

    x₂  = 7         and    y₂ = 1

Final answer:-

The co-ordinates of B are ( 7,1)

Find the product (x^2-2x-4)(x^2-3x-5)

Answers

The answer is 20 just took the test

The chemical acidity of a solution is measured in units of pH: pH=-log[H+], where [H+] is the hydrogen ion concentration in the solution. What is [H+] if the pH=8.8?

Answers

Answer:

3.5

Step-by-step explanation:

The chemical acidity of a solution is measured in units of pH: pH=-log[H+], where [H+] is the hydrogen ion concentration in the solution. 1.58 x 10⁻⁹ is [H+] if the pH=8.8.

What do you mean by pH ?

The term pH is defined as the negative logarithm of the [H+] hydrogen ion.

The isolated hydrogen ion, represented by the symbol H+, hence it is used to represent a proton. Because the bare nucleus can readily combine with other particles like electrons, atoms, and molecules, the  hydrogen ion.

The formula for calculating [H+] hydrogen ion is as follows:

pH = - log[H+]

Given pH = 8.8

8.8 = - log[H+]

-8.8 =  log[H+]

Taking Antilogarithm Both side

Antilog of [-8.8] = [H ]

By solving above expression [H+]

= 1.58 x 10⁻⁹

Thus, 1.58 x 10⁻⁹ is [H+] if the pH=8.8.

To learn more about the pH, follow the link;

https://brainly.com/question/15289741

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Montel uses 8 oz of sugar to make 36 fluid ounces of lemonade if it makes 180 fluid ounces of lemonade to bring to a party how many ounces of sugar will he use

Answers

Answer:

40 oz of sugar

Step-by-step explanation:

1) you have the basic measurement for 36 fluid ounces of lemonade, now imagine how many time can 36 go into 180 in order to find how many sugar oz you will need

180/36= 3

This mean 180 is 5 times as much lemonade and you will need 5 times as much sugar.

8ounces of sugar x 5 =  40ounces of sugar to make 180fluid ounces of lemonade

Jif peanut butter costs $3.29 for 16 oz. Skippy peanut butter costs $7.69 for 40 oz. Which is the better buy?

Answers

40 oz is better cause 3.29 x 2 is 6.58 for 32 oz add 8oz or 1.50 add you get 8.08

1.3.4b - What is the area of the composite polygon below? Be sure to include
proper units.
20 ft
12 ft
7 ft
8 ft
8 ft
34 ft

Answers

Show a picture please it would really help.

i’ll give brainliest

Answers

Answer: The line is dotted and shaded above

Three (3) movie tickets cost $36. At this rate, what is the cost per
ticket?
O $18
$33
O $12
O $108

Answers

$12 have a good day!! make sure u eat something!

Answer: 12$

Step-by-step explanation:

12X3 =36 , or 12 +12 +12 = 36

Solve the following compound inequality

Answers

Answer:

i believe your answer is correct

Step-by-step explanation:

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