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
Delvig [45]
3 years ago
15

Identify the vertex, axis of symmetry, maximum, or minimum, domain and range of each function.

Mathematics
1 answer:
Fynjy0 [20]3 years ago
6 0

Answer:  see below

<u>Step-by-step explanation:</u>

The vertex form of a quadratic equation is:    y = a(x - h)² + k     where

  • "a" is the vertical stretch (positive = min [U], negative = max [∩])
  • (h, k) is the vertex
  • Axis of Symmetry is always: x = h
  • Domain is always: x = All Real Numbers
  • Range is y ≥ k when "a" is positive or y ≤ k when "a" is negative

a) y = 2(x - 2)² + 5

        ↓       ↓      ↓

      a= +   h= 2   k= 5

Vertex: (h, k) = (2, 5)

Axis of Symmetry: x = h  →  x = 2  

Max/Min: "a" is positive → minimum

Domain: x = All Real Numbers

Range:  y ≥ k → y ≥ 5

b) y = -(x - 1)² + 2

        ↓       ↓      ↓

      a= -   h= 1   k= 2

Vertex: (h, k) = (1, 2)

Axis of Symmetry: x = h  →  x = 1  

Max/Min: "a" is negative → maximum

Domain: x = All Real Numbers

Range:  y ≤ k → y ≤ 2

c) y = -(x + 4)² + 0

        ↓       ↓      ↓

      a= -  h= -4   k= 0

Vertex: (h, k) = (-4, 0)

Axis of Symmetry: x = h  →  x = -4  

Max/Min: "a" is negative → maximum

Domain: x = All Real Numbers

Range:  y ≤ k → y ≤ 0

d) y = 1/3(x + 2)² - 1

        ↓       ↓      ↓

      a= +  h= -2   k= -1

Vertex: (h, k) = (-2, -1)

Axis of Symmetry: x = h  →  x = -2  

Max/Min: "a" is positive → minimum

Domain: x = All Real Numbers

Range:  y ≥ k → y ≥ -2

You might be interested in
100,000+4,000+800+5 in standard form.
Vedmedyk [2.9K]

Answer:

104,805 i think

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Expanded notation on algebra<br> 24 x 12 x 12
Delvig [45]

Answer:

3456

Step-by-step explanation:

24x12=288

288x12=3456

4 0
3 years ago
Hi What is the area of the object above?
WINSTONCH [101]
Dieikenfjdj dodkfkdkd dkdkfkdndd disk djdkd
7 0
3 years ago
Solve 15 ≥ -3x or 2/3 x ≥ -2.
hjlf
Solve each of the equations independently, then determine if the are continuous or discontinuous. 
15≥-3x [start here]
-5≤x    [divide both sides by (-3). *Dividing by a negative number means the direction of the sign changes!]
x≥-5  [just turned around for analysis]

Next equation:
2/3x≥-2    [start here]
x≥-2(3/2)  [multiply both sides of the equation by the reciprocal, 3/2)
x≥-3

So, (according to the first equation) all values of x must be greater than, or equal to -5.

(According to the second equation) all values of x must be greater than, or equal to -3. 
So, when graphed on a number line, both equations graph in the same direction, so they are continuous.

4 0
3 years ago
Read 2 more answers
The total cost to rent a row boat is $8 times the number of hours the boat is used. How long can you rent the boat for $176?​
MrMuchimi

Answer:

22 hours

Step-by-step explanation:

8•x= 176

Divide both sides by 8 and you get-

Y=22

3 0
3 years ago
Read 2 more answers
Other questions:
  • PLZ HELP ASAP WILL MARK BRAINIEST
    5·1 answer
  • I need help, what do I do?
    13·1 answer
  • What is 32gal/min=qt/h
    5·1 answer
  • 20 POINTS !! PLEASE ANSWER THIS QUESTION !! WILL GIVE BRAINLIEST !!
    5·2 answers
  • What is the circumference of the following circle when diameter = 9 cm
    9·2 answers
  • Luther owns a farm where he grows red and green tomatoes. He sells both types of tomatoes for $1.70 per pound . One customer bro
    13·1 answer
  • On a number line, point D is at -3, and point E is at 6. The point F lies on . The ratio of to is 2 : 3. Where does point F lie
    13·1 answer
  • The table shows the final score of four golfers.
    5·2 answers
  • I need help so bad please !!???
    12·1 answer
  • Help please <br> What is this expression in simplest form? <br> 4w/w-2 + 3w/w-3
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!