1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mr Goodwill [35]
3 years ago
14

Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x?

Mathematics
2 answers:
alisha [4.7K]3 years ago
6 0

Answer:

option A

f(x) = (x – 1)2 + 3

Step-by-step explanation:

Given in the question a function,

f(x) = 4 + x² – 2x

<h3>Step 1</h3>

f(x) = 4 + x² – 2x

here a = 1

        b = -2

        c = 4

<h3>Step 2</h3>

x = -b/2a

h = -(-2)/2(1)

h = 2/2

h = 1

Step 3

Find k

k = 4 + 1² – 2(1)

k = 3

Step 4

To convert a quadratic from y = ax² + bx + c form to vertex form,

y = a(x - h)²+ k

y = 1(x - 1)² + 3

y = (x - 1)² + 3

<h3></h3>

Mashutka [201]3 years ago
3 0

ANSWER

The vertex form is

f(x)  =  {(x - 1)}^{2}  + 3

EXPLANATION

The given function is

f(x)  = 4 +  {x}^{2}  - 2x

This is the same as:

f(x)  =  {x}^{2}  - 2x + 4

We add and subtract the square of half the coefficient of x.

f(x)  =  {x}^{2}  - 2x +  {( -1 )}^{2}  - {( -1 )}^{2}   + 4

f(x)  =  {x}^{2}  - 2x +  1    - 1  + 4

The first three term is a perfect square trinomial:

f(x)  =  {(x - 1)}^{2}    + 3

The vertex form is

f(x)  =  {(x - 1)}^{2}    + 3

You might be interested in
The initial population of a town is 1,300 and it is increasing at the rate of 3% each year. Find the population at 12 years​
stepan [7]

Answer:

1300 * (1 + 0.03)^12 = 1853

7 0
3 years ago
Read 2 more answers
Jenny multiplies the square root of her favorite positive integer by $\sqrt{2}$. Her product is an integer. a) Name three number
Dmitry [639]

Answer:

Part a) 2,50,18

Part b) When Jenny divides the square root of her favorite positive integer by \sqrt{2}, she gets an integer

Step-by-step explanation:

Let

x-------> the favorite positive integer

Part a)

1) For x=2

\sqrt{2}*\sqrt{2}=\sqrt{4}=2 -----> the product is an integer

so

The number x=2 could be Jenny favorite positive integer

2) For x=50

\sqrt{50}*\sqrt{2}=\sqrt{100}=10 -----> the product is an integer

so

The number x=50 could be Jenny favorite positive integer

3) For x=18

\sqrt{18}*\sqrt{2}=\sqrt{36}=6 -----> the product is an integer

so

The number x=18 could be Jenny favorite positive integer

Part B)

1) For x=2

\sqrt{2}/\sqrt{2}=\sqrt{1}=1 -----> the result is an integer

2) For x=50

\sqrt{50}/\sqrt{2}=\sqrt{25}=5 -----> the result is an integer

3) For x=18

\sqrt{18}/\sqrt{2}=\sqrt{9}=3 -----> the result is an integer

Therefore

When Jenny divides the square root of her favorite positive integer by \sqrt{2} , she gets an integer

4 0
3 years ago
I need to match each one to each other
kotegsom [21]

Answer

speed : metres per second (a)

perimeter : meters (b)

volume : cubic centimetres (d)

area : square metres (c)

4 0
3 years ago
Can y’all please help. I will send points if you want me to.
suter [353]

Answer:

the third one has a 2 acute angles 2 abuse angles and the x value is 110

Step-by-step explanation

the x value has to be bigger then 90 degree angles because it is a abuts angle and the 57 angle is a acute angle

8 0
3 years ago
There are nine tennis balls and three cans
tester [92]

Answer: 0.33 repeating


Step-by-step explanation: 3 divided by 9


6 0
3 years ago
Other questions:
  • X - 7 = 5x - 21
    8·2 answers
  • Assume body weight and height are related by the formula W=2H+13, where W represents weight in pounds and H represents height in
    10·1 answer
  • Which problems will have two decimal places in the product?mark all that apply.
    13·2 answers
  • Someone please help ASAP <br><br><br> a(x) = 7x^2+4x-5, <br> and b(x) = x - 4
    6·1 answer
  • Which list orders from least to greatest?
    9·1 answer
  • Castor bought 3 spells for $9 how many spells can you buy for $12.00
    13·2 answers
  • What is the measure of n?
    13·1 answer
  • Find the sum:(11x+3)+(x+-5)
    8·1 answer
  • Maria use 2/3 cups of powder mix every 2 gallons of water what is strength of the sports drink
    9·1 answer
  • A variable x has a binomial distribution with probability of success 0.3 for each trial.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!