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
Helen [10]
3 years ago
14

Given the functions f(x) = 4x2 − 1, g(x) = x2 − 8x + 5, and h(x) = –3x2 − 12x + 1, rank them from least to greatest based on the

ir axis of symmetry. A) g(x), h(x), f(x)
B) f(x), h(x), g(x)
C) g(x), f(x), h(x)
D) h(x), f(x), g(x)
Mathematics
1 answer:
tangare [24]3 years ago
7 0

Answer:

Option D) h(x), f(x), g(x)

Step-by-step explanation:

we know that

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex of the parabola

Part 1) we have

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

This is a vertical parabola open upward

The vertex is a minimum The vertex is the point (0,-1)

The x-coordinate of the vertex is 0

so

The axis of symmetry is x=0

Part 2) we have

g(x)=x^{2}-8x+5

This is a vertical parabola open upward

The vertex is a minimum

Convert the equation into vertex form

g(x)-5=x^{2}-8x

g(x)-5+16=x^{2}-8x+16

g(x)+11=x^{2}-8x+16

g(x)+11=(x-4)^{2}

g(x)=(x-4)^{2}-11

The vertex is the point (4,-11)

The x-coordinate of the vertex is 4

so

The axis of symmetry is x=4

Part 3) we have

h(x)=-3x^{2}-12x+1

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

h(x)-1=-3x^{2}-12x

h(x)-1=-3(x^{2}+4x)

h(x)-1-12=-3(x^{2}+4x+4)

h(x)-13=-3(x+2)^{2}

h(x)=-3(x+2)^{2}+13

The vertex is the point (-2,13)

The x-coordinate of the vertex is -2

so

The axis of symmetry is x=-2

Part 4) Rank their axis of symmetry from least to greatest

1) h(x) -----> axis of symmetry -2

2) f(x) -----> axis of symmetry 0

3) g(x) -----> axis of symmetry 4

so

h(x),f(x),g(x)

You might be interested in
-5+4y=-21 simplify your answer as much as possible <br>y=
nordsb [41]
4y=-21+5
4y=-16
y=4
simplified
3 0
3 years ago
Read 2 more answers
If a circle has a circumference of 103 find the arc inercepted by a central angle of 115
castortr0y [4]
360 divided by 115 = 3.13. Then you divide the 103 by the 3.13 = 32.90 
8 0
3 years ago
Fill in the blank to make each equality true. x/(1/2x^3)=16x^6 y^4
inn [45]

Answer:

ur in rsm too? i have the same question sorry -_-

Step-by-step explanation:

7 0
2 years ago
Which expressions are equivalent to q+p+q+p+qq+p+q+p+qq, plus, p, plus, q, plus, p, plus, q?
Vesnalui [34]

Answer:

A and B

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
on a trip, you had to change your money from dollars to British pounds. you got 560 pounds for 800 dollars. which is a unit rate
Bond [772]
1pound is 800/560......which is 80/56-->10/7
so 1 pound is 10/7 dollars....
because you don't say for one dollar it is this many pounds. 
also for unit rate i divide by 560 on both sides to get one pound on one side and then how many dollars on the other
6 0
2 years ago
Other questions:
  • Construct the 95% confidence interval for the population mean using the appropriate distributions. a. A random sample of 50 peop
    10·1 answer
  • Which is a factor of 144 − 49x2? HELP PLEASE
    5·2 answers
  • Find the common ratio for the following sequence. 0.1, 0.01, 0.001, ... 0.01 0.1 0.001
    14·1 answer
  • Somebody please help me on multiple step equations with parenthesis.
    15·1 answer
  • Find the measure of angle y in the following figure.
    11·1 answer
  • Solve the equation for y <br> 1/2y - 21/4 = -35/4
    10·1 answer
  • What is 3000×3000 4000
    13·2 answers
  • 1. What two key
    12·1 answer
  • If each 2 cm on the scale drawing equals 10 feet, what are the actual dimensions of the room? (5 points) Length = 11 feet, width
    10·2 answers
  • Value of 3 to the power of -2
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!