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
Serga [27]
3 years ago
11

The graph of y = x^2 -3 is translated in 4 units to the left of the graph to give the graph A

Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
4 0

Answer:

a) b = 8, c = 13

b) The equation of graph B is y = -x² + 3

Step-by-step explanation:

* Let us talk about the transformation

  • If the function f(x) reflected across the x-axis, then the new  function g(x) = - f(x)
  • If the function f(x) reflected across the y-axis, then the new  function g(x) = f(-x)
  • If the function f(x) translated horizontally to the right  by h units, then the new function g(x) = f(x - h)
  • If the function f(x) translated horizontally to the left  by h units, then the new function g(x) = f(x + h)

In the given question

∵ y = x² - 3

∵ The graph is translated 4 units to the left

→ That means substitute x by x + 4 as 4th rule above

∴ y = (x + 4)² - 3

→ Solve the bracket to put it in the form of y = ax² + bx + c

∵ (x + 4)² = (x + 4)(x + 4) = (x)(x) + (x)(4) + (4)(x) + (4)(4)

∴ (x + 4)² = x² + 4x + 4x + 16

→ Add the like terms

∴ (x + 4)² = x² + 8x + 16

→ Substitute it in the y above

∴ y = x² + 8x + 16 - 3

→ Add the like terms

∴ y = x² + 8x + 13

∴ b = 8 and c = 13

a) b = 8, c = 13

∵ The graph A is reflected in the x-axis

→ That means y will change to -y as 1st rule above

∴ -y = (x² - 3)

→ Multiply both sides by -1 to make y positive

∴ y = -(x² - 3)

→ Multiply the bracket by the negative sign

∴ y = -x² + 3

b) The equation of graph B is y = -x² + 3

You might be interested in
What is the measure of x? Help me on this Geometry question.​
AlladinOne [14]

Answer:

21°

Step-by-step explanation:

the angles of triangle abc has to = 180 so subtract the known angles to get 21

angles bca and daf have to be the same so its 21

8 0
3 years ago
Read 2 more answers
Please help me if you can. Please also write how you got the answer thank you.
vaieri [72.5K]

Answer:

The three numbers are 341, 342, and 343

Step-by-step explanation:

We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 1026. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 1026

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 1026

3X + 3 = 1026

3X + 3 - 3 = 1026 - 3

3X = 1023

3X/3 = 1023/3

X = 341

Which means that the first number is 341, the second number is 341 + 1 and the third number is 341 + 2. Therefore, three consecutive integers that add up to 1026 are 341, 342, and 343.

341 + 342 + 343 = 1026

We know our answer is correct because 341 + 342 + 343 equals 1026 as displayed above.

6 0
2 years ago
An underground conical tank has a top diameter of 4m and a depth of 6m. Compute the capacity of the tank in cubic meter.
dlinn [17]

Step-by-step explanation:

1/3πr^2h

{(1/3)×(22/7)×2^2×6}m^3

[(1/3)×(22/7)×4×6)}m^3

{528/21}m^3

=25.1 m^3

NOTE:r=diameter divided by 2

7 0
3 years ago
A circle is centered on Point B. Points A, C, and D lie on it’s circumference. If Angle ADC measures 61 Degrees, what does Angle
Nostrana [21]

Answer:

122

Step-by-step explanation:

61 x 2 = 122

6 0
3 years ago
Read 2 more answers
How many numbers between 100 and 999 are divisible by 4?
QveST [7]
Try this solution:
1. Note, that 100 is divisible by 4, and 999 is not divisible by it, only 996. This is an arithmetic sequence.
2. a1;a2;a3;a4;...a(n) the sequence, where a1=100; a2=104; a3=108; a4=112; ... etc., and a(n)=996. n=?
3. using a formula for n-term of the sequence: a(n)=a1+d(n-1), where a(n)=996; a1=100 and d=4 (according to the condition ' is divisible by 4'). Then 100+4(n-1)=996; ⇒ 4n=900; ⇒ n=225 (including 100).

answer: 225
7 0
3 years ago
Other questions:
  • Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. B = 74°, a
    12·2 answers
  • The endpoints of are A(1, 4) and B(6, -1). If point C divides in the ratio 2 : 3, the coordinates of C are . If point D divides
    7·2 answers
  • PLZ HELP WILL GIVE BRAINLIEST
    12·1 answer
  • If a person walks 16 miles in 10 minutes, how far will that person walk in one hour?
    9·2 answers
  • You are traveling from New York to los angeles to visit mickey mouse and his friends at disneyland. Given a map scale of 1 in. =
    7·1 answer
  • Gregory has 52 angelfish and 24 cichlid fish in his aquarium. Unfortunately, many of his fish got a sickness called "ick". 1/4 o
    6·1 answer
  • PLEASE HELP WITH THIS QUESTION​
    14·1 answer
  • Malcolm is working full-time and wants to make sure he's saving strategically for four specific goals: an emergency fund ($5000)
    9·1 answer
  • What does 1/5 + (-1/2) equal
    12·2 answers
  • What is the definition of cause and effect structure?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!