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
brilliants [131]
3 years ago
5

F(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, ∞) and g(x) = 2x2 + 8x + 6,

compare f(x) and g(x). Select the statement that is not correct?
A) Both functions have the same vertex.

B) Both functions have the same domain.

C) Both functions have the same x-intercepts.

D) Both functions are decreasing on the interval (−∞, −2).
Mathematics
2 answers:
svetlana [45]3 years ago
7 0

Answer:

B) Both functions have the same domain.

C) Both functions have the same x-intercepts.

D) Both functions are decreasing on the interval (−∞, −2).

Step-by-step explanation:

step 1

Find the vertex of f(x)

we know that

The x-coordinate of the vertex is the midpoint of the roots

we have

x=-1 and x=-3

so

the midpoint is

(-1-3)/2=-2

The y-coordinate of the vertex is -4 (because the range is [−4, ∞))

therefore

The vertex of f(x) is the point (-2,-4)

Is a vertical parabola open upward

The vertex is a minimum

The domain is all real numbers

step 2

we have

g(x)=2x^2+8x+6

Find the vertex

Factor the leading coefficient

g(x)=2(x^2+4x)+6

Complete the square

g(x)=2(x^2+4x+4)+6-8

g(x)=2(x^2+4x+4)-2

Rewrite as perfect squares

g(x)=2(x+2)^2-2

Is a vertical parabola open upward

The vertex is the point (-2,-2)

The domain is all real numbers

The range is the interval [−2, ∞)

Find the x-intercepts

For g(x)=0

0=2(x+2)^2-2

2(x+2)^2=2

(x+2)^2=1\\x+2=\pm1\\x=-2\pm1

so

The roots or x-intercepts are

x=-1 and x=-3

<u><em>Verify each statement</em></u>

A) Both functions have the same vertex

The statement is false

The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)

B) Both functions have the same domain.

The statement is true

The domain is all real numbers

C) Both functions have the same x-intercepts

The statement is true  (see the explanation)

D) Both functions are decreasing on the interval (−∞, −2)

The statement is true

Because the x-coordinate of the vertex is the same in both functions, and both functions open upward

kherson [118]3 years ago
7 0

Answer:

The answer is A

Step-by-step explanation:

You might be interested in
. Three professors examined awareness of four widely disseminated retirement rules among employees at University of Utah. These
Leya [2.2K]

Answer:

a) The population of interest = 10,000 benefited employees.  It includes all benefited employees.

b) The sample collected = 3,095.  These are the benefited employees who participated in the study.

c) Indication of demographic variables as categorical or numerical:

Demographic data:              Categorical or Numerical    

Gender                                = Categorical

Age (years)                          = Numerical

Education level                    = Numerical

 (years completed)

Marital status                       = Categorical

Household income ($)        = Numerical

Employment Category        = Categorical

Step-by-step explanation:

a) Data and Calculations:

Population of interest = 10,000 benefited employees

Sample = 3,095 participants

Demographic data:

Gender

Age (years)

Education level (years completed)

Marital status

Household income ($)

Employment Category

b) A variable is numerical value (e.g. length, test scores, etc.).  It is a continuous variable.  A categorical variable assumes a limited or fixed number of possible values, or it is categorized in groups.

8 0
2 years ago
HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION!!!!!!!!
ziro4ka [17]

Answer:

  • 80 tons
  • $20,000

Step-by-step explanation:

<u>21. 1st scenario</u>

  • B = fy + wz
  • 100,000 = 15,000*4 + 500w
  • 500w = 100,000 - 60,000
  • 500w = 40,000
  • w = 40,000/500
  • w = 80

80 tons of wheat

<u>22. 2nd scenario</u>

  • B = fy + wz
  • 50,000 = 2y + 200*50
  • 50,000 = 2y + 10,000
  • 2y = 50,000 - 10,000
  • 2y = 40,000
  • y = 20,000

Fighter plane's price is $20,000

8 0
3 years ago
Is the following relation a function?<br><br><br> x y<br> 1 4<br> −1 −2<br> 3 10<br> 5 16
Sergio [31]
No , because it doesn’t have a pattern . For example put the numbers in a chart 1+3 = 4 , -1+3 =2 , 3+7=10 , 5+11=16 , there’s no pattern
3 0
3 years ago
Which point on the number line best represents the location of root of 92.16
tatuchka [14]

Answer:

Point P

Step-by-step explanation:

9.59 is closer to 10 than 9, so we can safely say that points m and n cannot be correct. Point q can also not be correct, because it is to close to 10.

Therefore, answer is: Point P

5 0
3 years ago
A car rental company rents cars for x dollars per day plus y dollars for each mile driven. Carlos rented a car for 4 days, drove
topjm [15]

Answer:

x = $20/day, y = $0.35/mile

Step-by-step explanation:

x = $/day, y = $/mile

4x + 160y = 136

1x + 240y = 104

You can solve by elimination or substitution.

4 0
2 years ago
Other questions:
  • Which expressions are equivalent to 35 + 30s - 45t?
    10·2 answers
  • Between which two consecutive whole numbers does the square root 35 lie?
    15·1 answer
  • Write a problem that uses a fraction.
    9·2 answers
  • There are 16 marbles in a bowl: 3 are red, 6 are black, and 7 are green, Jimmy draws
    10·1 answer
  • I don't know how to do this.
    13·1 answer
  • You are a freshman in college and are planning a trip to Europe when you graduate from college at the end of four years. You pla
    7·1 answer
  • Let f(x)=x^2+5 and g(x)= (x+5)/x find (g fog f)(-3)
    15·1 answer
  • I NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I WILL GIVE BRAINLIST WHOEVER COMES FIRST Evaluate the expression if x = 9 and
    14·1 answer
  • Nineteen plus seven times the quantity of ten plus five, minus 4 to the third power
    12·2 answers
  • Which point is on the graph ofx=13(y−18)in the coordinate plane?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!