What does the quadratic function
f(x) = x2 - 6x + 8 look like when it is
rewritten in the form f(x) = a(x − p)2 +q?

Answers

Answer 1

Answer:

f(x) = (x -3)^2 - 1

Step-by-step explanation:

f(x) = x^2 - 6x + 8

a = 1, b = -6 and c = 8

So we are finding half of the b equation (ignore the negative sign)

Half of 6 is 3, so we are going to square 3 (3^2 = 9) and add 9 to the left side and subtract 9 to the right side

(x) = (x^2 - 6x + 9) + (8 - 9)

You can tell the polynomial is a perfect square, so we will have to factor it using the perfect square method

(x^2 - 6x + 9)

square toot of x^2 is x and square root of 9 is 3 and the operation sign after the a number is a minus sign

(x -3)^2

Don't forget the rest of the equation from before

(x -3)^2 + (8 - 9)

(x -3)^2 - 1

So the equation is f(x) = (x -3)^2 - 1


Related Questions

can someone please help me!

Answers

Answer:

60

Step-by-step explanation:

plz help ima freak out if I don't complete this

Answers

Answer:

2 and 3 are c you should try to do the others on your own they are just properties

Step-by-step explanation:

Answer:

2 and 3 are C, and 4 and 5 are B

Step-by-step explanation:

Which expression is equivalent to 3(x - 2)+2x?
-X
3x
5x - 2
5x -6

Answers

Hey there!

The answer to your question is the third option; [tex]5x-6[/tex]

First, we'll start by simplifying your expression. Given:

[tex]3(x - 2)+2x[/tex]

Distribute the [tex]3[/tex]:

[tex]3x-6+2x[/tex]

Add [tex]3x[/tex] and [tex]2x[/tex]:

[tex]5x-6[/tex]

Therefore, the third option is correct.

Have a terrificly amazing day! :)

At the carnival, it costs $10 to enter. It then costs $1.50 per ride you go on.
If you have $28, how many rides can you go on? *
1 point

Answers

Answer:

18.6

Step-by-step explanation:

28 divided by 1.50 equals 18.6

The number of rides will be equal to 12 in the Carnival.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that at the carnival, it costs $10 to enter. It then costs $1.50 per ride you go on. The total amount is $28.

The number of rides will be calculated by forming an equation below,

A = 10 + 1.5R

28 - 10 =1.5R

1.5R = 18

R = 18 / 1.5

R  = 12

Therefore, the number of rides will be equal to 12 in the Carnival.

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Find the missing values

Answers

I FOUND THEM THEY ARE HIDING IN THE CLOUDS.

10. Write 144 with an exponent by using 12
as the base.


Answers

Answer:

12^12

Step-by-step explanation:

According to a weather report, there is a 28% chance it will rain tomorrow. What is the
probability that it WILL NOT rain tomorrow? (two decimal answer approximation)

Answers

Answer:

wouldnt it be 72%?

Step-by-step explanation:

the percent is out of 100. if the probability of rain is 28% and you subtract that from 100% you are left with 72%

100%-28%

=72%

Brainliest for correct answer

Answers

Answer:

what grade are you in im in 10th and idek know this

Step-by-step explanation:

use PEMDAS btw it help

Answer:

X=-4

Step-by-step explanation:

Do number six for me.

Answers

The answer is c
The sum of the triangle angles is 180
So 180-80-40=60
180-(60+80)=40


12. In y > x + 4, where can we find the solution set?
A. above the line
C. in the line
B. below the line
D. no solution set

13. The statement, "the sum of two numbers is at least 29" can be expressed as:
A. x + y > 29 B. x + y < 29 C. x + y = 29 D. x + y = 2

14. The elevator has a maximum capacity (C) of 8 persons. Which of the following mathematical statement represent the given situation?
A.C = 8
B. C < 8
C. c 28
D. none of these

15. Bryan bought 6 chocolate candies and 3 lollipops. If x represent the cost of
chocolate candies and y represent the cost of lollipops, what will be the
mathematical representation of the total cost if he paid at most Php50?
A.6x + 3y > 50
C. 6x + 3y > 50
B.6x + 3y = 50
D. 6x + 3y < 5​

Answers

Answer:

1) D

2)A

3)D

4)A

Step-by-step explanation:

PLEASE MARK ME AS BRAINLIEST

Answer:

I hope I can help you

Step-by-step explanation:

I hope I can help you

Simplify the ratio 0.3:0.48

Answers

Answer:

0.1:0.16

Step-by-step explanation:

they can both be divided by 3

.48/3=.16

.3/3=.1

PLEASE HELP ME!!!!
what is the first quartile of the set of data shown below? 16,23,25,39,45,78,95

Answers

Answer:

23

Step-by-step explanation:

What is the explicit rule for the sequence?

10.5, 9, 7.5, 6, 4.5, 3, ...

Answers

answer: the rule is to add 1.5

3 + 1.5 = 4.5
4.5 + 1.5 = 6
6 + 1.5 = 7.5
etc...

I know this might be a easy answer but with proper algebra format a chicken has two legs a dog has 4 legs the chicken must have 14 more legs than the dog And it has to add up to 28 legs this is easy but I wanna know how to get the answer

Answers

Step-by-step explanation:

Let each let of chicken be C and dog be D respectively.

Then as per question

2C+4D = 28.......i

and

C-D =14........ii

These are the two algebraic equation which you are looking for solve them

to get the answer

the hypotenuse of a triangle is 5in and leg one is 4in how long is leg two

Answers

So you do a^2+b^2=c^2 so hypotenuse is the longest long so it is c and other leg can be b or a it doesn’t matter as long as you have 5 for c so a^2+4^2=5^2
a^2+16=25
I squared the numbers 4times4=16 and 5times5=25
Now you minus 16 because we are trying to figure out what “a” is or other words leg two
So 25-16=9
Now a is still square so be got to take the square 2 away and square 2 is also know as square root so a= 3 the other leg is 3
Check
3^2+4^2=5^2
9+16=25
25=25

Daysi buys a video game on sale. If the video usually costs $30.00, and it
was on sale for 25% off, how much did Daysi pay?

Answers

Answer:

$22.5

Step-by-step explanation:

The original price is $30 and it's on sale for 25% off.  Since 25% is a quarter of the total price, I divided 30÷4=7.5.  $7.5 is 25% of $30, so 7.5 is the amount taken off the original price.  To find what Daysi paid, I subtracted 30-7.5=22.5.  $22.5 is the result after the 25% off, so Daysi paid $22.5.  

PLEASE PUT THE FOLLOWING IN ORDER
tysm

Answers

Y = 500x + 38000 would be the first step, as that sets up the equation. Then, 45500 = 500x + 38000 would be the next. Third would be 7500 = 500x, as that is where we subtract 38000 from both sides. Then, finally the answer is x = 15.
To put it in a list
1. Y = 500x + 38000
2. 45500 = 500x + 38000
3. 7500 = 500x
4. 15 = x meaning 15 air conditioners must be sold

Answer:

yessuh

Step-by-step explanation:

Solve each system by substitution.
y=-4x-9 y=3x+19

Answers

Answer:

x=-4, y=7

Step-by-step explanation:

According to the first equation, y = -4x - 9, so we can substitute y in the second equation for -4x - 9.

y = 3x + 19

-4x - 9 = 3x + 19

Add 9 to both sides

-4x = 3x + 28

Subtract 3x

-7x = 28

Divide by -7

x = -4

Plugging this into the equation, we have:

y = -4x - 9

y = -4(-4) - 9

y = 16 - 9

y = 7

Can someone do this please

Answers

Answer:

x = [tex]\sqrt{5}[/tex]

Step-by-step explanation:

[tex](\sqrt{21} )^{2}[/tex] = 4^2 + ^2

21 - 16 = x^2

x = [tex]\sqrt{5}[/tex]

Multiply Fractions and Whole Numbers

7 x 2/3 =

Show me your work

Answers

14/3 = 4 2/3 - simplified

The simplified form of the Multiplication of Fractions and Whole Numbers would be  4 2/3.

What is a fraction?

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).  When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction. A proper fraction is also called fraction which is less than 1.

Given that the fraction expression as;7 x 2/3

We need to multiply Fractions and Whole Numbers

7 x 2/3 = 14/3

Now convert simple fraction into mixed;

14/3 = [tex]4 \frac{2}{3}[/tex]

Therefore, the simplified form of the Multiplication of Fractions and Whole Numbers would be  [tex]4 \frac{2}{3}[/tex].

Learn more about fraction;

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Of the 10 clients who had their hair cut at Sue's salon last month, 5 had blond hair. Considering this data, how many of the next 14 clients to get haircuts should you expect to have blond hair?

Answers

Answer: 7 clients

Step-by-step explanation:

Of the last 10 clients that cut their hair at the salon, 5 had blond hair.

That is a proportion of:

= 5 / 10

= 1/2

Assuming this same proportion applies to the next clients Sue gets, the expected number of blonde people will be:

= Number of clients * 1/2

= 14 * 1/2

= 7 clients

plz help thannkkk you so muchh

Answers

This is a bit strange how your teacher mentions the height increases at 10 inches per minute, but then doesn't refer to the time value afterward.

Ignoring that oddity, we have [tex]V = \pi*r^2*h[/tex] turn into [tex]V = \pi*4^2*h[/tex] when plugging in r = 4. This simplifies to [tex]V = 16\pi*h[/tex]

This represents the volume V for any given height h.

Let's plug in [tex]V = 80\pi[/tex] and solve for h

[tex]V = 16\pi*h\\\\80\pi = 16\pi*h\\\\80 = 16*h\\\\80/16 = h\\\\5 = h\\\\h = 5[/tex]

Note: in the jump from step 2 to step 3, I divided both sides by pi.

So we found that when the height is h = 5 feet, this leads to the volume being [tex]V = 80\pi[/tex] cubic feet.

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

Let's convert from feet to inches

1 foot = 12 inches

5 feet = 60 inches (multiply both sides by 5)

The height of the cylinder is 60 inches when the volume is 80pi cubic feet.

We're told that the height increases by 10 inches per minute. This would mean that h = 10t assuming the height starts at 0 when the time value is t = 0.

Solving for t leads to...

h = 10t

60 = 10t

60/10 = t

6 = t

t = 6

After 6 minutes, the height is 60 inches = 5 feet.

an urn contains 10 blue marbles and 8 yellow marbles a marble is drawn and dropped back into the urn. Then a second marble is drawn and dropped back into the urn both marbles are yellow if another marble is drawn. what is the probability that it will be blue

Answers

Answer:

80/729

Step-by-step explanation:

8/18x8/18x10/18=640/5832

80/729

Can someone solve this please: 54.69 rounded to the nearest integer

thank you <3​

Answers

Answer:

55

Step-by-step explanation:

55
Rounding up to an integer is rounding up to a whole number, 55 would be the nearest whole number!

How do I solve this question

Answers

Answer:

/2

Step-by-step explanation:

A store offers 30% off all items. If x is the original purchase price, select all of the expressions which represent the final price with the discount.
a 0.7x
b x
c x + 0.3x
d x - 0.3x
e 12x

Answers

Answer:

D c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

not really an explanation

what is the additive inverse of -15 and 15

Answers

For -15 its 15, and for 15 it's -15

Answer

-15

Step-by-step explanation:

What is a decimal that is equivalent to the fraction 8/10
? Enter the answer in the box.

Answers

Answer:

0.8

Step-by-step explanation:

Answer:

.8

Step-by-step explanation:

luca sells muffins and juice boxes. muffins are $1.50 each and jucie boxes are $1.25 each. write an algebraic expression for the total income luca received from the sale of muffins and juice boxes​

Answers

Answer:

1.5m+1.25j

Step-by-step explanation:

m equals the number of muffins sold, and because each muffin sells for $1.50, 1.5m represents the income made from the muffins.

Same thing with the juice boxes, j equals the number of juice boxes sold, and because each juice box sells for $1.25, 1.25j represents the income made from the juice boxes.

Add the income from both of them to get the total income, and you get 1.5m+1.25j.

Free Pls help
Question: Solove for X

Answers

I'm sorry, I thought I could have helped. I hope you have a nice day!

X=13 is the answer I think
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