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
BigorU [14]
3 years ago
15

For the function below, find the vertex, axis of symmetry, maximum or minimum value, and the graph of the function.

Mathematics
2 answers:
const2013 [10]3 years ago
6 0
F(x) = x^2/2 + 2x + 1f(x) = 1/2 * (x^2 + 4x) + 1f(x) = 1/2 * (x^2 + 4x + 4) - 1/2 * (4) + 1f(x) = 1/2 * (x + 2)^2 - 1
The vertex is (-2, -1). The axis of symmetry is x = -2. The minimum value is -1. The maximum value is infinity.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

amm18123 years ago
3 0

Answer and Explanation :

Given : Function f(x)=\frac{x^2}{2}+2x+1

To find : The vertex, axis of symmetry, maximum or minimum value, and the graph of the function.

Solution :

The quadratic function is in the form, y=ax^2+bx+c

On comparing, a=\frac{1}{2} , b=2 and c=1

The vertex of the graph is denote by (h,k) and the formula to find the vertex is

For h, The x-coordinate of the vertex is given by,

h=-\frac{b}{2a}

h=-\frac{2}{2(\frac{1}{2})}

h=-\frac{2}{1}

h=-2

For k, The y-coordinate of the vertex is given by,

k=f(h)

k=\frac{h^2}{2}+2h+1

k=\frac{(-2)^2}{2}+2(-2)+1

k=2-4+1

k=-1

The vertex of the function is (h,k)=(-2,-1)

The x-coordinate of the vertex i.e. x=-\frac{b}{2a} is the axis of symmetry,

So, x=-\frac{b}{2a}=-2 (solved above)

So, The axis of symmetry is x=-2.

The maximum or minimum point is determine by,

If a > 0 (positive), then the parabola opens upward and the graph has a minimum at its vertex.

a=\frac{1}{2} >0 so,  the parabola opens upward and the graph has a minimum at its vertex.

The Minimum value is given at (-2,-1)

Now, We plot the graph of the function

At different points,

x          y

-4        1

-2        -1

0         1

Refer the attached figure below.

You might be interested in
Use the grouping method to factor x^3+x^2+3x+3
maks197457 [2]

Answer:

(x^2 + 3)(x + 1).

Step-by-step explanation:

x^3 + x^2 + 3x + 3

= x^2(x + 1) + 3(x + 1)

= (x^2 + 3)(x + 1).

7 0
3 years ago
Q2) If z is directly proportional to x and z = 12 when x = 3, find the value of x when z = 18.
LenKa [72]

Answer:

4.5

Step-by-step explanation:

→ Set up the direct proportion equation

z = kx

→ Substitute in the values

12 = 3k

→ Divide both sides by 3 to isolate k

4 = k

→ Substitute the value of k back into the original direct proportion equation

z = 4x

→ Substitute the value of z in

18 = 4x

→ Divide both sides by 4 to isolate x

4.5 = x

4 0
3 years ago
Read 2 more answers
9. Find the point of intersection of the lines: y = 4x + 1 and y = - 2x + 4 A. (2,9) B.(1/2,3) C. (1,2) D. (1/4,2)
Colt1911 [192]

Step-by-step explanation:

y = 4x + 1 and y = -2x + 4

4x + 1 = -2x + 4, 6x = 3, x = 0.5

When x = 0.5, y = 4(0.5) + 1 = 3.

The point of intersection is (0.5, 3). (B)

3 0
3 years ago
Read 2 more answers
what are the coordinates of the image of the point (–3, 6) after a dilation with a center of (0, 0) and scale factor of 1/3 a. (
dybincka [34]
It's gotta be C.) I'm pretty sure
3 0
3 years ago
Read 2 more answers
In the following expression, n is a rational number: Which expression below is equivalent to this expression?
gogolik [260]

Answer:

none of them

Step-by-step explanation:

7 0
1 year ago
Other questions:
  • A baby woolly mammoth that was discovered in 2007 died approximately 39,000 years ago. How many C-14 atoms
    5·1 answer
  • 10+2(x - 7) - 4+3(x+6) - 1 (distributive property)
    11·1 answer
  • A circle is inscribed in an equilateral triangle. A point in the figure is selected at random. Find the probability that the poi
    6·1 answer
  • There are 42 students 21 are in 7th grade 14 are in 8th 7 are in ninth whats the probability of an eighth grader winning
    6·1 answer
  • The difference of 4 and 5 times h ​
    12·2 answers
  • PLEASE HELP ASAP
    6·1 answer
  • 3 bananas cost $0.33. At this rate, how much do 5 bananas cost?
    6·1 answer
  • GARDENING A gardener uses a grow light to grow vegetables indoors. If m∠1=(8x)° and m∠2=(7x−4)°, what is m∠1?
    6·2 answers
  • Accrual income versus cash flow for a period. Thomas Book Sales, Inc., supplies textbooks to college and university bookstores.
    15·1 answer
  • What is the slope? (5,6) and (-1, 4)
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!