A quadratic function has x-intercepts 2 and 6 and its vertex is (4, 8). What is the corresponding quadratic expression? A. 2x2 − 16x + 24 B. -2x2 + 16x – 24 C. -2x2 - 16x + 24 D. -x2 − 16x + 12 E. -x2 − 16x – 24

Answers

Answer 1

Given:

A quadratic function has x-intercepts 2 and 6 and its vertex is (4, 8).

To find:

The corresponding quadratic expression.

Solution:

If graph of a function intersect the x-axis at c, then (x-c) is a factor of the function.

A quadratic function has x-intercepts 2 and 6. It means (x-2) and (x-6) are two factors of the required quadratic function.

The function is defined as:

[tex]P(x)=a(x-2)(x-6)[/tex]                    ...(i)

Where, a is a constant.

The vertex of the quadratic function is (4,8). It means the point (4,8) will satisfy the function.

Substituting x=4 and P(x)=8 in (i).

[tex]8=a(4-2)(4-6)[/tex]

[tex]8=a(2)(-2)[/tex]

[tex]8=-4a[/tex]

Divide both sides by -4.

[tex]\dfrac{8}{-4}=a[/tex]

[tex]-2=a[/tex]

Putting [tex]a=-2[/tex] in (i), we get

[tex]P(x)=-2(x-2)(x-6)[/tex]

[tex]P(x)=-2(x^2-6x-2x+12)[/tex]

[tex]P(x)=-2(x^2-8x+12)[/tex]

[tex]P(x)=-2x^2+16x-24[/tex]

Therefore, the correct option is B.


Related Questions

Describe the relationship between ∠2 and ∠8

Answers

Answer:

Alternate Interior Angles

Step-by-step explanation:

Angles can be corresponding; alternate or same side; or interior or exterior. The angles 2 and 8 are on opposite sides of the transversal; this means that they must be alternate angles. Additionally, they are both within the parallel lines, so they are interior. Alternate interior angles are always congruent. Therefore, their measurements must be equal.

Answer:

They are alternate interior angles

Step-by-step explanation:

<2 and <8 are inside the parallel lines and on opposite sides of the transversal

They are alternate interior angles

What’s the measure of POQ?

Answers

Answer: 70 degrees 35 times 2

what is 200x149 who can answer that for me i need help on this my teacher said i cant use couculater

Answers

Answer:

29,800

Step-by-step explanation:

that will be 149 x 2 which equals 298

149

 ×2         Multiply 9 × 2 = 18

------        Keep the 8 carry the 1 multiply 4 by 2 then add 1 finally multiply 2 by 1

298

Then add two zeros at the end since we're multiplying a number with two zeros. (This method only works for numbers that end with zeros)

Final answer: 29800

Use pascal triangle to expand and simplify (5x+4y)³​

Answers

Answer:

125x³+240xy²+64y³ +300yx²

Step-by-step explanation:

Row of pascals triangle to use is 1 3 3 1

For binomial expansion, use a³ +3a²b+3ab²+b³

40 POINTS!!!
All integers are either odd or even. Conceptually, an integer is odd if it has a remainder of 1 when dividing by 2. And an integer is even if it has a remainder of 0 when dividing by 2.

But when proving something rigorously, mathematicians use more precise definitions, like these: an integer is odd if it can be written in the form 2k + 1, where k is some integer. An integer is even if it can be written in the form 2k, where k is some integer. For example, 13 is odd because 13 can be written as 2(6) + 1.

With these definitions, use complete sentences to explain why zero is an even number.

Answers

Answer:

[tex] = > 2k + 1 \\ when \: k = 0 \\ 2(0) + 1 \\ = 1 \\ \therefore \: zero \: is \: odd \\ \\ = > 2k \\ when \: k = 0 \\ 2(0) \\ = 0 \\ \therefore \: zero \: is \: not \: even \: because \: when \: divided \: by \: 2 \: \: remainder \: is \: zero[/tex]

Wow what grade are you in? Cause this is so much, sorry

An artist made a 54-inch-tall statue of a former president. If the president was 6 feet tall, what scale did the artist use?

Answers

Answer:

[tex]1\text{ inch}=\frac{1}{9}\text{ foot}[/tex]

Step-by-step explanation:

To get a scale of inches to feet, divide both 54 and 6 by 54:

[tex]54\:\text{inches}=6\:\text{feet},\\\implies 1\:\text{inch}=\frac{6}{54}\:\text{ft}\implies \boxed{1\:\text{inch}=\frac{1}{9}\:\text{foot}}[/tex]

Mike needs to replace the carpet in his living room. The carpet he likes costs $7.50 per square foot to purchase and install. His living room measures 263.5 square feet. How much will it cost to replace the carpet?

Answers

Answer:

$1,976.25

Step-by-step explanation:

Since one square foot cost $ 7.50 we simply multiply that by 263.5.

263.5 × 7.50= $1,976.25

Find the product of (2x-3)(x-1)​

Answers

Answer:

Step-by-step explanation:

[tex](2x -3)(x-1) = 2x(x-1) -3(x-1)[/tex]

                     [tex]=2x^2 -2x -3x +3\\= 2x^2 - 5x + 3[/tex]

Use the sum of cubes identity to write this polynomial expression in factored form:
8x3 + 27.

Answers

Answer:

[tex] {8x}^{3} + 27 \\ = {8x}^{3} + {3}^{3} \\ let : 8x \: be \: a \\ : 3 \: be \: b \\ = > {a}^{3} + {b}^{3} : \\ {(a + b)}^{3} = (a + b)( {a}^{2} + 2ab + {b}^{2} ) \\ {(a + b)}^{3} = ( {a}^{3} + 3{a}^{2} b + 3a {b}^{2} + {b}^{3} ) \\ ( {a}^{3} + {b}^{3} ) = {(a + b)}^{3} - 3ab(a + b) \\ \therefore( {8x}^{3} + 27) = {(8x + 3)}^{3} - 72(8x + 3)[/tex]

8 cm
10 cm
The surface area of the above figure is
A. 816.8 cm2
B. 879.6 cm2
C. 565.5 cm2
D. 1131.0 cm2

Answers

Answer D from the web

1. Find the value of x to the nearest tenth

A. 8.1
B. 7.5
C. 8.9
D. 7.9

Answers

Answer:

C.

[tex]x = 2( \sqrt{ {6}^{2} - {4}^{2} } ) \\ x = 2( \sqrt{20} ) \\ x = 8.9[/tex]

Find the measure of DAE

Answers

I can't see the picture, can you add it again so I can help?

I know how do it but the fraction is confusing me please help will give branliest

Answers

Replace x and y in the equation with what they tell you x and y equal.

2(14) / 13 - 9(1/3)

Now simplify:

2 x 14 = 28

9 x 1/3 = 3

You now have:

28/13-3

Simplify again to het 28/10 this can be reduced to 14/5

Integer x is evenly divisible by 3. Which expression below is also evenly divisible by 3?

A. 2x+ 1
B. 3x-5
C. 4x-1
D. 4x+6

Answers

Hi! I’m not positive, but I believe it would be D., 6 is the only one that is evenly divided by 3. Once again I’m not positive, I’m only a middle schooler so.... yeah.

Use the Pythagorean theorem to find the missing length in the right triangle

Answers

C^2 = a^2 + b^2

In this case your a is 24 and b is 7

That means c = sqaure root of(24^2 + 7^2)

C = 25

Answer:

Hi, there your answer is 25

Step-by-step explanation:

Here's the Pythagorean Theorem formula [tex]a^{2} +b^{2}=c^{2}[/tex]

[tex]7^{2}+24^{2}[/tex]=[tex]c^{2}[/tex]

49+576=[tex]c^{2}[/tex]

625=[tex]c^{2}[/tex]

[tex]\sqrt{625}=c^{2}[/tex]

[tex]25=c[/tex]

Hope this helps :)

Solve the equation of 5(3−4)=8+15

Answers

Answer:

-5 ≠ 23

Step-by-step explanation:

5(3−4)=8+15

5(-1) = 8 + 15

-5 = 23

-5 ≠ 23


The dimensions of triangular prom are shown in the diagram
10 cm
10 cm
cm
34 cm
-12 cm
What is the total surface area of the triangular prism in square centimeters?
A 1,184 sq cm
B 1,632 sq cm
C 3,264 sq cm
D 32,640 sq cm

Answers

Answer:

1,184 sq cm

Step-by-step explanation:

Surface area= 2 (1/2 x 8 x 12 + 34 x 10) + 34 x 12

                    = 1,184 sq cm

Hope this helps!

Please help me with this geometry question and show work

Answers

(3) 8

Step-by-step explanation:

Note that ∆ADE is similar to ∆ABC. As such, the ratios of their legs are equal. Also note that AD = AB + BD.

BC/AB = DE/AD

BC/10 = 12/(10 + 5) = 12/15 = 4/5

or

BC = 10(4/5) = 8

A telephone technician charges $45.00
per hour plus a $50.00 service charge.
Your father's firm hires him to hook up
his company's phone system.
Here is the cost function used to
represent this situation in terms of the
number of hours worked:
c(h) = 45h + 50
Find the total charges if it takes the telephone 4.5 hours to complete the task

Answers

252.5 is the answer to this question

Part A

Whose scatter plot matches the data, and what is wrong with the incorrect scatter plot?

Answers

Answer: hello your question has some missing data attached below is the missing data

answer:

The second scatter plot

Step-by-step explanation:

The scatter plot that matched the data is the second scatter plot while the first scatter plot wrongly represents the data because values of the Iron not present in the data is also represented in the scatter plot and also some values present in the data table is also missing in the First scatter plot

Answer:

Hello, I am currently doing the same assignment and the brothers scatter plot would be wrong.

Step-by-step explanation:

If you do not believe me then check and see how the table says the iron used were 2, 3, 4, 5, 6, 7, 8, and 9 but in the brothers scatter plot it is shown to have the irons down as 1, 2, 3, 4, 5, 6, 7, and 8.

(in other words the other person who answered is correct)

How to solve this? I have no clue and also teach me on how to solve this! Thank you!!! thank you for your time!!!!

Answers

The answer you have is the correct answer. When reflecting across the x-axis, the x-coordinate will always remain the same, but the y-coordinate value will be the opposite (in this case -5 will become 5)

Please help??? An explanation would help too and the answers

Answers

the first, (f+g)(x) is f(x) + g(x)

calculating it like:

x² + 7x + (8 -x²)

= x² + 7x + 8 -x²

= 7x + 8

you just writ it down as a calculation and calculate it. i hope that helps understanding the concept/basic idea. please let me know wich ones you need more help with.

edit1: the domain is the range of possibilities wich x we can plug into the new equation

Can someone help I’m confused

Answers

Answer:

D and E

Step-by-step explanation:

Let's double check:

D. 9 ÷ 3 = 3

E. 4 × 9 = 36

---------------------------------------------------------------------------------------------------------------

Have a great summer :)

Answer:

the answers would be A, D, and E

Step-by-step explanation:

just replace the Cs with the number 9 and solve from there.

for example c/3=3 would say 9/3=3


someone please help

Answers

Answer:

sqrt(106) =c

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

5^2 +9^2 = c^2

25+81 = c^2

106 = c^2

Taking the square root of each side

sqrt(106)= sqrt(c^2)

sqrt(106) =c

Answer:

Length of missing side is 10.44/ √106.

Step-by-step explanation:

Here we have

A right triangle with

1st side = a = 5

2nd sidd = b = 9

and , we need to find 3rd side of triangle

let the 3rd side be x.

Using Pythagoras theorem

a ² + b ² = c ²

( 5 ) ² + ( 9 ) ² = ( c)²

25 + 81 = ( c) ²

106 = ( c) ²

Taking square root of each side

√106 = √ c ²

√106 = c

10.44 = c

So, missing side if triangle is 10.44 /√106.

Can someone help me with these problems and explain them as well please

Answers

Answer:

b=112°

Step-by-step explanation:

two complementary angles

b=180°-68°=112°

sum of 2 angles is

x= 35°+25°=60°

Answer:

3. b=112

4. x = 60

Step-by-step explanation:

3.

b is equal to 112 since 68+b will be equal to a supplementary angle; an angle that adds up to 180. 180-68 is equal to 112.

4.

35+25 = 60, therefore x = 60.


The equation of the line that has a slope and passes through the point (-1, -3) is 3x + 2y +3 = 0.

Answers

Answer:

below

Step-by-step explanation:

that is the procedure above

Please help me I put 100 points for anyone who helps me

Answers

Answer:

a)

The discount id 40%, so the function is:

d = 0.4p

b)

p = 100 ⇒ d = 40p = 200 ⇒ d = 80p = 300 ⇒ d = 120p = 400 ⇒ d = 160p = 500 ⇒ d = 200

The graph is attached

c)

p = $85 ⇒ d = 0.4*$85 = $34

Sale price is:

CP = p - d = $85 - $34 = $51

Answer:

please give me some thanks please good morning

Can someone help me out with these few problems 1,3,4,6,7,10,12,15
Please only reply back if you really are trying to help me please no spam
I would really appreciate it

Answers

Answer:

Step-by-step explanation:

1) the complete squares of the picture are 12, if we unite the other we can reach 15 squares circa

15 * 50 = 750 square units

3) Area = base x height = 12 * 9 = 108 cm^2

4) Area = (base x height)/2 = (24 * 16)/2 = 192 in^2

6) Area of the square = side ^ 2 = 12^2 = 144 cm^2

height of the triangle = 20 - 12 = 8 cm

Area of the triangle = (base x height)/2 = (12 * 8)/2 = 48 cm^2

Total area = 144 + 48 = 192 cm^2

7) radius = diameter / 2 = 20 : 2 = 10 cm

circumference = radius * 2 * pi = 20 * pi = 62.8 cm

area = radius^2 * pi = 100 * pi = 314.2 cm^2

10) √25 = 5

we have to find a  positive number that multiply by itself gives 25

12) √100 = 10

we have to find a positive number that multiply by itself gives 100

15) √64 = 8

we have to find a positive number that multiply by itself gives 64

a, I see, you split the workload :D

this answer is just a greeting,making you able to choose a brainliest.

if someone leaves a greeting in the other topic, it works there to. :D

Question is due soon I need help

Answers

Answer:

looks like C is best guess

A ​$108,000 down payment would be? of the purchase price.

Answers

Answer: 10.8%

Step-by-step explanation:

The question is asking what the percentage of the down payment is of the purchase price of the house.

For such a question, the purchase price needs to be known.

We shall therefore assume a purchase price and you can use the process to find out your percentage.

Assume the purchase price is $1,000,000.

The percentage would be:

= Down payment / Purchase price * 100%

= 108,000 / 1,000,000

= 10.8%

Answer:

10.8%

Step-by-step explanation:

see above

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