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
aniked [119]
3 years ago
10

Identify the axis of symmetry and vertex of f(x) = –2x2 –2x–1.

Mathematics
2 answers:
Leya [2.2K]3 years ago
4 0

<span>Given the quadratic equation: f(x) = -2x^2 - 2x - 1, the axis of symmetry can be obtained by finding the line that divides the function into two congruent or identical halves. Thus, it should pass through the vertex and is equal to the x-coordinate of the vertex. </span>

<span>Note that a quadratic equation in standard form: y = ax^2 + bx + c, has the vertex located at (h,k) where, h = -b/2a and k is determined by evaluating y at h. In this case, a = -2, b = -2, thus, h = -0.5, k = 0.5. Thus, the vertex is located at (-0.5, 0.5) and the axis of symmetry is at x = -0.5. </span>

MakcuM [25]3 years ago
3 0

Answer:

Part A) The vertex is the point (-0.5,-0.5)

Part B) The axis of symmetry is x=-0.5

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

y=a(x-h)^{2}+k

where

(h,k) is the vertex of the parabola

and the axis of symmetry is equal to the x-coordinate of the vertex

so

x=h -----> equation of the axis of symmetry

In this problem we have  

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

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

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

Factor the leading coefficient

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

Complete the square. Remember to balance the equation by adding the same constants to each side

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

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

Rewrite as perfect squares

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

f(x)=-2(x+(1/2))^{2}-(1/2) -----> equation in vertex form

The vertex of the parabola is the point (-0.5,-0.5)

Is a vertical parabola open downward

The axis of symmetry is equal to

x=-0.5

see the attached figure to better understand the problem

You might be interested in
David, Malachy and Paul share some sweets in the ratio 5:4:1. David gets 20 more sweets than Paul. How many sweets does Malachy
White raven [17]

Answer:

16

Step-by-step explanation:

ratio is 5:4:1

David: Malachy: Paul

David gets 20 (that is 4 times more than the original ration. so need to multiply everything by 4)

4*4=16

1*4=4

new ration- 20:16:4

So David gets 20

Malachy gets 16

Paul gets 4

7 0
3 years ago
Find the surface area of the prism.
boyakko [2]

Answer:

156 [in²].

Step-by-step explanation:

1) total area consists of six parts (all the details are in the attachment):

A=2A₁+2A₂+A₃+A₄;

2) according to the formula above:

A=2*5*3+2*0.5*(6+12)*4+6*3+12*3=156 [in²].

6 0
2 years ago
SO basically uhh I suck at math
postnew [5]
Ok so you plug them in. -5 squared is 25 minus 27
6 0
3 years ago
Read 2 more answers
The circle is inscribed in Triangle AEC. Which are congruent line segments
Harlamova29_29 [7]

Answer:

E-F and E-D

C-B and C-D

Step-by-step explanation:

The circle and triangle are as shown.  The options are:

  • A-B and C-B
  • E-F and E-D
  • E-D and C-D
  • A-F and E-F
  • C-B and C-D

By drawing radius lines from the center of the circle to the tangent points B, D, and F, we can divide the triangle into 3 kites.  Therefore, only segments that are legs of the same kite are congruent.  So the answer must be E-F and E-D, and C-B and C-D.

6 0
3 years ago
Read 2 more answers
Solve the following systems by substitution
Paladinen [302]

Answer:

The answer to your question is below

Step-by-step explanation:

Question 1

                x = 5                       Equation l

                2x + y = 10              Equation ll

- Substitute Equation l in equation ll

               2(5) + y = 10

                y = 10 - 10

                y = 0

- Solution  (5, 0)

Question 2

                 x + 16y = 20          Equation l

                 x = 4y                    Equation ll

Substitute equation ll in equation l

                4y + 16y = 20

                        20y = 20

                           y = 20/20

                           y = 1

-Find x

                x = 4(1)

                x = 4

-Solution

                (4, 1)

Question 3

                   2x + 8y = 20            Equation l

                     x = 2                       Equation ll

-Substitute equation ll in equation l

                   2(2) + 8y = 20

                      4 + 8y = 20

                            8y = 20 - 4

                            8y = 16

                              y = 16/8

                              y = 2

- Solution

                   (2, 2)              

8 0
3 years ago
Other questions:
  • I received a letter from your competitor that mentions a savings of 15% over your prices. Can you match this offer? My current r
    14·1 answer
  • What is 59.69 written in expanded form
    10·2 answers
  • What is the probability Jane gets a cone with any ice cream and any topping?
    13·2 answers
  • What is the value of x?<br><br><br><br> Enter your answer in the box.<br><br> x =
    10·2 answers
  • 0.09502 to 2 decimal places
    12·1 answer
  • You are dealt one card from a standard 52-card deck. Find the probability of being dealt a red card
    11·1 answer
  • Which type of triangle will always have at least 1-fold reflectional symmetry?
    13·2 answers
  • 4. Steve worked 37.5 hours last week for $15.00 an hour. What is his gross pay for the<br> week?
    6·1 answer
  • IMA DO BRAINLYST AFTER IM DONE I PROMISE BUT TY FOR ALL HELP THERES STILL MORE
    12·1 answer
  • If 6 pairs of socks cost $6. 90, what is the price for one pair of socks
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!