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
ozzi
3 years ago
14

Graph f(x) = x2 + 2x - 3, label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and lab

el the axis of symmetry

Mathematics
1 answer:
Semenov [28]3 years ago
5 0
<h2>Answer with explanation:</h2>

The given function : f(x)=x^2+2x-3

Using completing the squares, we have

f(x)=x^2+2x+1-1-3        [∵ (x+1)^2=x^2+2x+1]

f(x)=(x+1)^2-4      (1)

Comparing (1) to the standard vertex form f(x)=(x-h)^2+k , the vertex of function is at (h,k)=(-1,-4)

For x-intercept, put f(x)=0 in (1), we get

0=(x+1)^2-4\\\\\Rightarrow\ (x+1)^2=4    

Square root on both sides, we get

x+1=\pm2\\\\x+1=-2\ or\ \ x+1=2\\\\=x=-3\ \ or\ x=1

∴ x intercepts : x= (-3,0) and (1,0)

For y-intercept put x=0 in (1), we get

f(1)=(1)^2-4=1-4=-3  

∴ y intercept : (0,-3)

Axis of symmetry : \dfrac{-b}{2a}

In f(x)=x^2+2x-3 , a=1 and b=2

Axis of symmetry=\dfrac{-2}{2(1)}=-1

You might be interested in
Gloria has a $125,000 home financed with a 30-year loan at 6%. If she wished to pay one extra monthly payment each year, how man
musickatia [10]

295 months. AAAAPPPPEEXXX sucks I know.

3 0
3 years ago
[10] In the following given system, determine a matrix A and vector b so that the system can be represented as a matrix equation
irina1246 [14]

Answer:

y=-\frac{158}{579}

Step-by-step explanation:

To find the matrix A, took all the numeric coefficient of the variables, the first column is for x, the second column for y, the third column for z and the last column for w:

A=\left[\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right]

And the vector B is formed with the solution of each equation of the system:b=\left[\begin{array}{c}3\\-3\\6\\1\end{array}\right]

To apply the Cramer's rule, take the matrix A and replace the column assigned to the variable that you need to solve with the vector b, in this case, that would be the second column. This new matrix is going to be called A_{2}.

A_{2}=\left[\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right]

The value of y using Cramer's rule is:

y=\frac{det(A_{2}) }{det(A)}

Find the value of the determinant of each matrix, and divide:

y==\frac{\left|\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right|}{\left|\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right|} =\frac{158}{-579}

y=-\frac{158}{579}

7 0
3 years ago
Reflect triangle ABC over the x-axis. Then translate the new triangle 5 units to the left. What are the coordinates of the verti
makvit [3.9K]

Hi there!

The answer to your question is B my explanation is below

The coordinates of the vertices of the final image will be:

A''(-6, 8), B''(-7, -2), and C''(0, -2)

Hence, option (B) is true.

Step-by-step explanation:

Given the triangle with the vertices

A(-1, -8)B(-2, 2)C(5, 2)We know that when we reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate reverses its sign.

Thus,

The rule of reflection across the x-axis:

(x, y) → (x, -y)

so

A(-1, -8) → A'(-1, -(-8)) = A'(-1, 8)

B(-2, 2) → B'(-2, -2) = B'(-2, -2)

C(5, 2) → C'(5, -2) = C'(5, -2)

Then, translate the new triangle 5 units to the left

Rule of translating 5 units to the left

(x, y) → (x-5, y)

so

A'(-1, 8) → A''(-1-5, 8) = A''(-6, 8)

B'(-2, -2) → B''(-2-5, -2) = B''(-7, -2)

C'(5, -2) → C''(5-5, -2) = C''(0, -2)

Therefore, the coordinates of the vertices of the final image will be:

A''(-6, 8), B''(-7, -2), and C''(0, -2)

Hence, option (B) is true.

8 0
3 years ago
Read 2 more answers
Mark and his three friend's ate at Applebee's. Their bill totaled $52.35. if they left the server a 20% tip, how much would each
kompoz [17]
Check the attachment.

6 0
3 years ago
tiffany has breakfast at a restaurant and the cost of her meal is $27.00.because of the service.she wants to leave a 10% tip.wha
Bess [88]

27*.1= 2.70

27+2.70= 29.70 Total bill

3 0
3 years ago
Other questions:
  • Please help and thank you
    6·1 answer
  • Jamie is a salesperson in a shoe store and earns $95 per week, plus 20% of her weekly sales. If Jamie makes $475 in one week, wh
    10·1 answer
  • Someone lmk what the answer is
    11·1 answer
  • What is the percent 200 percent of 8.5
    15·2 answers
  • Can you reduce 7 over 28
    5·2 answers
  • Is it A)50 degrees, B) 60 degrees C) 74 degrees or D) 78 degrees
    8·2 answers
  • Given the diagram below solve for x
    15·1 answer
  • Please please please help me with math
    5·1 answer
  • Hola me pueden ayudar por favor es de matemáticas
    7·2 answers
  • 14. A bag contains 20 marbles. There are 4 blue
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!